Nanotechnology for Electronics, Photonics, and Renewable Energy

Nanostructure Science and Technology

Series Editor David J. Lockwood

For further volumes: http://www.springer.com/series/6331

Anatoli Korkin · Predrag S. Krsti´c · Jack C. Wells Editors

Nanotechnology for Electronics, Photonics, and Renewable Energy

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Editors Anatoli Korkin Nano and Giga Solutions, Inc. Gilbert, AZ 85296, USA [email protected]

Predrag S. Krsti´c Physics Division Oak Ridge National Laboratory P.O. Box 2008 Oak Ridge, TN 37831, USA [email protected]

Jack C. Wells Oak Ridge National Laboratory Center for Engineering Science Advanced Computational Nanotechnology Group P.O. Box 2008 Oak Ridge, TN 37831, USA [email protected]

ISSN 1571-5744 ISBN 978-1-4419-7234-7 e-ISBN 978-1-4419-7454-9 DOI 10.1007/978-1-4419-7454-9 Springer New York Dordrecht Heidelberg London Library of Congress Control Number: 2010939003 © Springer Science+Business Media, LLC 2010 All rights reserved. This work may not be translated or copied in whole or in part without the written permission of the publisher (Springer Science+Business Media, LLC, 233 Spring Street, New York, NY 10013, USA), except for brief excerpts in connection with reviews or scholarly analysis. Use in connection with any form of information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed is forbidden. The use in this publication of trade names, trademarks, service marks, and similar terms, even if they are not identified as such, is not to be taken as an expression of opinion as to whether or not they are subject to proprietary rights. Printed on acid-free paper Springer is part of Springer Science+Business Media (www.springer.com)

Preface

Tutorial lectures given by world-renowned researchers have become one of the important traditions of the Nano and Giga Challenges (NGC) conference series. Soon after preparations had begun for the first forum, NGC2002,1 in Moscow, Russia, the organizers realized that publication of the lectures notes would be a valuable legacy of the meeting and a significant educational resource and knowledge base for students, young researchers, and senior experts. Our first book was published by Elsevier and received the same title as the meeting itself—Nano and Giga Challenges in Microelectronics.2 Our second book, Nanotechnology for Electronic Materials and Devices,3 based on the tutorial lectures at NGC20044 in Krakow, Poland, the third book from NGC20075 in Phoenix, Arizona, and the current book from joint NGC2009 and CSTC20096 meeting in Hamilton, Ontario, have been published in Springer’s Nanostructure Science and Technology series. Hosted by McMaster University, the meeting NGC/CSTC 2009 was held as a joint event of two conference series, Nano and Giga Challenges (Nano & Giga Forum) and Canadian Semiconductor Technology Conferences (CSTC), bringing together the networks and expertise of both professional forums. Informational (electronics and photonics), renewable energy (solar systems, fuel cells, and batteries), and sensor (nano and bio) technologies have reached a new stage in their development in terms of engineering limits to cost-effective improvement of current technological approaches. The latest miniaturization of electronic devices is approaching atomic dimensions. Interconnect bottlenecks are limiting circuit speeds, new materials are being introduced into microelectronics manufacture at an unprecedented rate, and alternative technologies to mainstream CMOS are being considered. The low cost of natural energy sources and ignorance of the limits and environmental impact from use of natural carbon-based fuels have been long-standing economic barriers to the development of alternative and more efficient solar systems, fuel cells, and batteries. Nanotechnology is widely accepted as a source of potential solutions in securing future progress in information and energy technologies. Nanotechnology as the art (i.e., science and technique) of control, manipulation, and fabrication of devices with structural and functional attributes smaller than 100 nm is perfectly suited to advanced CMOS technology. This technology

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holds the capacity for massive production of high-quality nanodevices with an enormous variety of applications from computers to biosensors, from cell phones to space shuttles, and from large display screens to small electronic toys. Driven by scaling electronic devices to smaller and smaller sizes, the electronic industry has developed a set of sophisticated methods for deposition of ultra-thin films with very precise composition and nanoscale lithographic patterning. Enormous investment in nanotechnology for electronics R&D from companies and governments of many developed countries now finds a “new source of revenue”— solar energy applications. Based on the same core materials—silicon and other semiconductors—photovoltaics has for a long time been a "poor relative" of microand optoelectronics. That is not the case any more. The need for clean and renewable energy is becoming evident for the global community from the limited resources of mineral fuel and from the growing environmental impact of our current highly wasteful use of natural resources. Moreover, the world-wide energy crisis may spark a global political crisis and threaten the existence of human civilization. The success of the NGC/CSTC 2009 conference, which resulted in the publication of this book and in other contributions making up special issues of Nanotechnology7 and Nanoscale Research Letters,8 would not have been possible without generous support from many sponsors and research institutions. We gratefully acknowledge the contributions and support of McMaster University (conference host and co-organizer), Arizona State University, Springer, Canadian Ministry of Foreign Affairs and Trade, Russian Nanotechnologies Corporation, Nokia, Oak Ridge National Lab, Ontario Centres of Excellence, Sematech International, CMC Microsystems, and many other local, national, international, and individual supporters. Gilbert, Arizona Oak Ridge, Tennessee Oak Ridge, Tennessee

Anatoli Korkin Predrag S. Krsti´c Jack C. Wells

Notes 1 http://asdn.net/ngcm2002/ 2 Nano

and Giga Challenges in Microelectronics, eds. J. Greer, A. Korkin, J. Labanowski (Elsevier, Amsterdam, Netherlands, 2003) 3 Nanotechnology for Electronic Materials and Devices, eds. A. Korkin, E. Gusev, J. Labanowski, S. Luryi (Springer, New York, USA, 2007) 4 http://asdn.net/ngcm2004/ 5 http://asdn.net/ngc2007/ 6 http://asdn.net/ngc2009/ 7 Selected and invited papers from NGC/CSTC 2009 symposium on semiconductor technology (guest editors Stephen Goodnick, Anatoli Korkin, Predrag Krstic, Peter Mascher, John Preston, and Alexander Zaslavsky) published in Nanotechnology 21(13) (2010)

Preface

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8 Nanoscale science and technology for electronics, photonics and renewable energy

applications: Selected papers from NGC2009 & CSTC2009 conference. (guest editors Anatoli Korkin, Predrag Krstic, Zoran Miskovic, Hongbin Yu, and Igor Zhitomirsky) published in the open-access journal, Nanoscale Research Letters 5(3) (2010).

Contents

1 Molecular Electronics: Challenges and Perspectives . . . . . . . . . Paolo Lugli, Simone Locci, Christoph Erlen, and Gyorgy Csaba 2 Three-Dimensional Silicon–Germanium Nanostructures for CMOS-Compatible Light Emitters . . . . . . . . . . . . . . . . . D.J. Lockwood and L. Tsybeskov

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3 On Application of Plasmas in Nanotechnologies . . . . . . . . . . . . Zoran Lj. Petrovi´c, Paul Maguire, Marija Radmilovi´c-Radjenovi´c, Maja Radeti´c, Nevena Puaˇc, Dragana Mari´c, Charles Mahony, and Gordana Malovi´c

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4 All Carbon Nanotubes Are Not Created Equal . . . . . . . . . . . . Gyula Eres, D.B. Geohegan, A.A. Puretzky, and C.M. Rouleau

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5 Two Routes to Subcellular Sensing . . . . . . . . . . . . . . . . . . . G.F. Cerofolini

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6 Photothermal Sensing of Chemical Vapors Using Microcantilevers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Thomas Thundat, Charles W. Van Neste, Larry R. Senesac, and Adam R. Krause

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7 Nanoelectronics for DNA Sensing . . . . . . . . . . . . . . . . . . . . Predrag S. Krsti´c

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8 Nanostructured Electrode Materials for Lithium-Ion Batteries . . . A. Manthiram and T. Muraliganth

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9 Synthetic Models of Copper Proteins for Biofuel Cell Applications . Dominic F. Gervasio

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Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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Contributors

G.F. Cerofolini CNISM and Department of Materials Science, University of Milano–Bicocca, 20125, Milano, Italy Gyorgy Csaba Institute for Nanoelectronics, Technische Universität München, D80333, Munich, Germany Gyula Eres Materials Science and Technology Division, Oak Ridge National Laboratory, Oak Ridge, TN 37831, USA Christoph Erlen Institute for Nanoelectronics, Technische Universität München, D80333, Munich, Germany D.B. Geohegan Materials Science and Technology Division, Oak Ridge National Laboratory, Oak Ridge, TN 37831, USA Dominic F. Gervasio Department of Chemical and Environmental Engineering, University of Arizona, Tucson, AZ 85721, USA Adam R. Krause Nanoscale Science and Devices Group, Oak Ridge National Laboratory, Oak Ridge, TN 37831, USA Predrag S. Krsti´c Physics Division, Oak Ridge National Laboratory, Oak Ridge, TN 37831, USA Simone Locci Institute for Nanoelectronics, Technische Universität München, D80333, Munich, Germany D. J. Lockwood Institute for Microstructural Sciences, National Research Council Canada, Ottawa, Ontario K1A 0R6, Canada Paolo Lugli Institute for Nanoelectronics, Technische Universität München, D80333, Munich, Germany Paul Maguire Nanotechnology and Integrated BioEngineering Centre, University of Ulster, Newtownabbey, Co Antrim, BT37 OQB, UK Charles Mahony Nanotechnology and Integrated BioEngineering Centre, University of Ulster, Newtownabbey, Co Antrim, BT37 OQB, UK

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Gordana Malovi´c Institute of Physics, University of Belgrade, 11080, Zemun, Serbia A. Manthiram Materials Science and Engineering Program, The University of Texas at Austin, Austin, TX 78712, USA Dragana Mari´c Institute of Physics, University of Belgrade, 11080, Zemun, Serbia T. Muraliganth Materials Science and Engineering Program, The University of Texas at Austin, Austin, TX 78712, USA Zoran Lj. Petrovi´c Institute of Physics, University of Belgrade, 11080, Zemun, Serbia Nevena Puaˇc Institute of Physics, University of Belgrade, 11080, Zemun, Serbia A.A. Puretzky Materials Science and Technology Division, Oak Ridge National Laboratory, Oak Ridge, TN 37831, USA Maja Radeti´c Faculty of Technology and Metallurgy, University of Belgrade, 11000, Belgrade, Serbia Marija Radmilovi´c-Radjenovi´c Institute of Physics, University of Belgrade, 11080, Zemun, Serbia C.M. Rouleau Materials Science and Technology Division, Oak Ridge National Laboratory, Oak Ridge, TN 37831, USA Larry R. Senesac Nanoscale Science and Devices Group, Oak Ridge National Laboratory, Oak Ridge, TN 37831, USA Thomas Thundat Nanoscale Science and Devices Group, Oak Ridge National Laboratory, Oak Ridge, TN 37831, USA L. Tsybeskov Department of Electrical and Computer Engineering, New Jersey Institute of Technology, University Heights, Newark, NJ 07102-9895, USA Charles W. Van Neste Nanoscale Science and Devices Group, Oak Ridge National Laboratory, Oak Ridge, TN 37831, USA

Chapter 1

Molecular Electronics: Challenges and Perspectives Paolo Lugli, Simone Locci, Christoph Erlen, and Gyorgy Csaba

Abstract Molecular electronics has lately attracted increasing attention due to some appealing features such as possibly very higher integration capabilities, their low production cost, flexibility in the substrate choice, and possibility for large-area deployment. Two parallel approaches characterize this field: on one side molecules can be contacted and their transport characteristics exploited to achieve electronic functionalities; on the other side existing device structures, as well as novel ones, can be realized using organic layers instead of or together with inorganic materials. While in the latter case theoretical investigations on such devices can be carried out on adapting conventional simulators to the new materials and physics involved, completely new tools have to be developed in the former case. In this chapter, the operational principles of molecular systems will be presented based on a series of theoretical results obtained from our groups. Challenges and perspectives are also discussed.

Introduction Molecular electronics has witnessed increased interest in recent years, triggered by the forecast that silicon technology might reach its scalability limits in a few years [1–4]. In order for molecular electronics to become a valuable alternative to silicon technology, it will not be sufficient to fabricate molecular electronic devices with outstanding characteristics, but appropriate circuit and architectural solutions will also be needed. While a lot of effort has been dedicated to the demonstration of electronic functionalities of single molecules and organic films, research at the circuit and system level is still in its infancy [5–9]. Investigation on single molecules or nanotube-based devices promises to keep Moore’s law alive once miniaturization of silicon-based structures becomes P. Lugli (B) Institute for Nanoelectronics, Technische Universität München, Arcistrasse 21, D80333 Munich, Germany e-mail: [email protected]

A. Korkin et al. (eds.), Nanotechnology for Electronics, Photonics, and Renewable Energy, Nanostructure Science and Technology, DOI 10.1007/978-1-4419-7454-9_1,  C Springer Science+Business Media, LLC 2010

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impractical. As first proposed by Aviram and Ratner [10], one can imagine to squeeze entire nonlinear circuit elements (such as diodes or transistors) into single molecules. In principle, such devices could be significantly faster and smaller than end-of-the-roadmap solid-state electron devices. Despite an enormous progress on the experimental characterization of single-molecule conduction in the last years, only few device concepts have emerged and it is still unclear whether individual molecular devices could be integrated into a larger-scale computing circuit. In any case, we can be sure that molecular circuits and architectures will be very different from what we are used to in today’s systems. Several architectures, which would be suitable for the realization of electronic logic circuits or memory cells based on molecular devices, have been proposed. One possibility is to synthesize complex molecules whose arms can be separately contacted to provide the same electrical input/output of conventional logic gates. Such fascinating idea, suggested by Ellenbogen and Love [11], is unfortunately extremely challenging from the chemical-synthesis point of view, and it has not been realized up to now. Another possibility is to create a programmable interconnected network of nanoparticles and molecular entities (“nanocells”) [12]: conducting metallic nanoparticles are randomly deposited on a substrate (which can be a silicon one) and subsequently bridged via molecular connections, to create electrical pathways between previously patterned metallic leads. The molecular linkers should exhibit nonlinear IV characteristics, in the form of negative differential resistance or hysteretic behavior and the network is connected to a limited number of input/output pins at the edges of the nanocell, which could then be accessed, configured, and programmed from the edges. Simulations have demonstrated the capability of the nanocell to act as logic gate [12, 13]. Integration with CMOS technology will certainly be the first step for devices based on single molecules, with solutions that follow a road that has been called “More than Moore” [14], in an attempt to extend the standard chip functionalities already offered by silicon technology. Such hybrid systems would benefit from the speed and reliability of CMOS, while offering at the same time the versatility and intrinsically nanometer footprint of molecular devices. Two architectures which are in principle compatible with silicon technology are the “Quantum Cellular Automata” [15] and the “cross bar” [16, 17]. While the latter employs solutions based on standard interconnections, the former relies on a highly innovative approach. In fact, devices and their interconnections can no longer be separated in a straightforward way in single-molecule electronics and it is not clear if the paradigm of classical circuit theory for building a complex system can still be followed [18, 19]. It is very timely to explore alternative ideas to interconnect molecular building blocks inside the molecular circuit and the molecules to the outer world without metal wires [20], using electric or magnetic fields. One very interesting hybrid architecture is the semiconductor/nanowire/molecular one (“CMOL”), proposed by Likharev and coworkers [21, 22]. The basic difference with respect to crossbars is that in CMOL the interface between CMOS circuitry and nanowires is provided by pins distributed all over the circuit area. Thus, a much larger integration should be achieved, with relaxed requirement concerning alignment of the wire interconnects.

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Besides single-molecule structures, molecular electronics refers also to the employment of organic materials as substitutes for the solid-state layers of traditional semiconductor devices. Since their carrier mobility is relatively low, organic devices cannot compete with silicon-based circuits in high-speed, high-performance computing applications, but can become competitive in the market of large-area devices, because their process technology is potentially inexpensive and circuits can be realized on virtually any substrate (e.g., on plastics, paper, or textiles) [23]. We will present our theoretical analysis on organic transistors, inverters, and ring oscillators, describing the simulation tools used and its applications to device and circuit modeling. In the areas of chemical sensing, light emission, and light sensing, organic materials could make far more versatile devices as their semiconductor counterparts, because of the wide selection of possible sensor and light-emitting materials [24]. The first products have already entered the marketplace (e.g., OLEDdisplays), whereas others will follow soon. Due to their versatility in terms of fabrication and performance, organic films could also be integrated with silicon circuitry, embracing again the “More than Moore” paradigm. Modeling and simulation of these device classes, which imitate traditional solid-state devices with organic materials, seems quite straightforward, as the existing semiconductor simulation approaches, like the well-established drift-diffusion method [25], can be applied. In spite of many open issues, mainly related to the charge transport in organic semiconductors as well as to their morphology [26], simulating organic devices do not require the development of fundamentally new approaches. In parallel to numerical simulation, analytical approaches have also been developed, which can help in the analysis of transport phenomena (e.g., trapping) and device operation [27]. Circuits employing organic thin-film transistors (OTFTs) are based on the same building block of conventional electronics, namely the inverter, but, due to the difficulty of realizing n-type organic transistors, typical circuits rely only on p-type devices, without being of complementary types [28]. A quite different approach is required for single-molecule devices, where quantum mechanical tools are needed. Quantum chemistry methods have reached a high level of maturity and are credited with good predictive power for the determination of formation energies and molecular geometries. It seems natural to extend these methods beyond their original purpose to treat non-equilibrium transport processes through single (or few) molecules and to analyze their device performance. To such purpose, density functional theory (DFT) [29] usually provides the description of the electronic properties of the molecular system, while the non-equilibrium Green’s function (NEGF) [30] allows one to compute the transport characteristics. With such tools, it is possible to calculate the current–voltage characteristics of a molecule connected to two metallic electrodes [31, 32]. Due to the computational complexity of the DFT–NEGF algorithms, it is basically impossible to extend them to the design of even very elementary circuits and memory cells. It is therefore necessary to develop approaches which allow us to go from the atomistic description of the single molecular element to design tools capable of full circuit simulations. Construction of equivalent circuit models and circuit-level simulations serve this purpose [33], as will be discussed afterwards.

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Single Molecules Electronic conduction through a variety of different molecules has been studied experimentally by many research groups [31, 32, 34–36] and novel design architectures for memories and logic circuits have been explored. However, the exact nature of the transport mechanisms in many of such systems remains still open to scientific debate. To correctly treat these problems, complex ab initio computations are needed. First-principles computations [29, 37, 38] are normally based on density-functional methods, which are, however, limited to molecular systems made up of a small number of atoms. In addition, a precise estimation of energy band gaps requires sophisticated many-body corrections. Since we are interested in the transport properties of molecules, which are not isolated entities but rather connected to metallic electrodes, we need first to clarify how the interactions between molecule and contacts determine the energy levels of the complete system. We have used the density-functional tight-binding (DFTB) method [39, 40–45], which allows a first-principles treatment of systems comprising a large number of atoms. This method, implemented in the code gDFTB, has been extended to the nonequilibrium Green’s function (NEGF) approach [30], by generalizing the calculation of the atomic charges using the non-equilibrium (DFT) density matrix and solving a three-dimensional Poisson solver [40]. The implementation of NEGF is similar to other codes based on first-principles approaches [46, 29]. Thus, the computation of the tunneling current between two contacts is possible in a manner consistent with the open boundaries and non-equilibrium conditions that naturally arise in coherent transport problems. The main approximations of gDFTB are (i) the use of limited basis functions (mainly the minimal basis) and (ii) the use of two-center approximation in the calculation of the Hamiltonian matrix elements. The use of such approximations makes the scheme computationally extremely fast and makes the approach suitable to treat systems with several thousands of atoms, thus applicable to nanostructured devices. The gDFTB scheme can be considered as a highly efficient high-level computational tool which works surprisingly well despite the large number of simplifying assumptions. It enables, for instance, the computation of the tunneling current flowing between two or more contacts in a manner consistent with the open boundaries and non-equilibrium conditions that naturally arise in coherent transport problems. Molecular dynamics simulation can be performed within the present approach, and time-dependent currents can be calculated accounting for molecular vibration effects [40, 47]. Recently, the approach has also been extended to account for electron–phonon interactions [48]. The density-functional tight-binding (DFTB) formalism has been described in detail in many articles and reviews [49]. All matrix elements and orbital wavefunctions are derived from density-functional calculations. The advantage of the method relies on the use of a small basis set and the restriction to two center integrals, allowing extensive use of look-up tables. What distinguishes our approach from empirical methods is the explicit calculation of the basis wavefunctions, which allows deeper physical insights into and better control of the approximations used.

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The method solves the Kohn–Sham equations self-consistently using a Mulliken charge projection [43]. In the traditional DFTB code a minimal basis set of atomic orbitals is used in order to reduce the matrix dimensions for diagonalization speedup. This approach has proved to give transferable and accurate interaction potentials, and the numerical efficiency of the method allows molecular dynamic simulations of large super-cells, containing several hundreds of atoms, particularly suitable to study the electronic properties and dynamics of large mesoscopic systems and organic molecules such as CNTs, DNA strands or adsorbates on surfaces, and semiconducting heterostructure [50]. We briefly describe here the self-consistent DFTB method. The electronic density is expanded as a sum of a reference density n0 (r) (that can be chosen as the superposition of neutral atomic densities) and a deviation, δn(r), such that n(r) = n0 (r) + δn(r). The total energy of the system can be described, up to second order in the local density fluctuations, as        Etot [n] = nk ψk H 0  ψk + Erep n0 + E(2) [δn]. (1.1) k

The first term in Eq. (1.1) can be written in terms of the TB Hamiltonian, which is given by 

0 free−atom H  μν = εμ  ,   μ = ν ,   0 0 φμ T + veff ni + nj  φν , μ ∈ i, ν ∈ j

(1.2)

where φ μ and φ ν are the atomic orbitals localized around the atomic centers i and j; T is the kinetic energy operator; and veff is the effective one-particle potential, which depends on the density of the two atomic centers i and j. The term Erep n0 in Eq. (1.1) is the repulsive energy between the ions, screened by the electronic distribution and the exchange energy. The third term in Eq. (1.1) is the second-order correction that can be written as

 1 1 δ 2 Exc 2  + (1.3) δn(r)δn(r ) dr dr , E [δn] = r − r  δn(r)δn(r ) 2 where the Hartree and exchange–correlation potentials have been separated. This quantity is greatly simplified by retaining only the monopole term in the radial expansion of the atom-centered density fluctuations [51]. Within the LDA approximation the exchange contribution vanishes for large atomic distances. Hence in Eq. (1.3) the second-order correction to Exc can be neglected with respect to the Coulomb interaction. For short ranges Coulomb and XC contributions are accounted with on-site Hubbard parameters, which are calculated for any atom type within LDA-DFT as the second derivative of the total energy of the atom with respect to the occupation number of the highest occupied atomic orbital. These values are therefore neither adjustable nor empirical parameter [43]. By applying the variational principle to the energy functional of Eq. (1.1),

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it is possible to obtain a modified Hamiltonian for the Kohn–Sham equations:   1 0 + Sμν γik + γjk qk , ∀μ ∈ i, ν ∈ j, Hμν = Hμν 2

(1.4)

k

where Sμν is the overlap matrix between atomic wavefunctions, γik is a shorthand for the interatomic potential [51], computed from Eq. (1.3), and qk are the atomic charges. Since the atomic charges depend on the one-particle wave functions ψ k , a self-consistent procedure is required. The improvement of the self-consistent over the non-self-consistent procedure is considerable in determining structural and energetic properties of molecular systems [43]. The DFTB approach has been extended to the NEGF formalism by generalizing the calculation of the atomic charges using the non-equilibrium (DFT) density matrix and computing the functional (1.3) using a three-dimensional Poisson solver [47, 49, 52]. Despite its mathematical complexity, the non-equilibrium Green’s function (NEGF) for calculations of quantum transport has gained great popularity in recent years, mostly because of the versatility and numerical stability of the method, in contrast to wavefunction or transfer matrix approaches. The open boundary conditions can be elegantly included by exactly mapping the contacting leads into a finite and small part of the system [53]; furthermore, the Green’s function approach can be generalized to many-body quantum theory, allowing the inclusion of electron–phonon [54] as well as electron–electron interactions [55] within a unified and systematic formalism. Good references in many-body quantum theory can be found in [56, 57] and an exhaustive review on NEGF can be found in [58].

Transport in OPVs We have applied the gDFTB code to the study of molecular transport through oligopolyvinylene (OPV) chains anchored to metallic contacts [59]. OPV molecules consist of benzene rings which are interconnected by vinylene groups (Fig. 1.1 for a 5-ring OPV structure). A DFT-based investigation of the transport properties of short OPV wires (up to five rings) has been presented in [60]. We concentrate here on longer structures. The electronic transport characteristics of the OPV molecules

Fig. 1.1 OPV molecule with five rings bonded to gold contacts by a sulfur atom. From: [59] Copyright Wiley-VCH Verlag GmbH & Co. KGaA. Reproduced with permission

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are governed by the electronic states available in the molecule. Such states can be effectively described by the local density of states (LDOS), which represents the equilibrium density of states existing in the molecular device broken down into the contributions of single atoms or ensembles of atoms of the device. The gDFTB code calculates the LDOS of each atom by projecting the density of states of the total structure on the molecular orbitals of this atom. Figure 1.2 shows the LDOS for OPVs of different lengths. The broadening of the molecular levels (with respect to the sharp peaks that would be found for isolated molecules) is a result of the covalent bonding between the molecular device and the contacts or the adjacent sulfur atoms and is related to a finite lifetime of electrons on the corresponding orbitals. Such finite lifetime is crucial for current flow to appear, as will be emphasized in the following. The LDOS peaks of the molecules are getting sharper with increasing wire length. The associated longer lifetime of the electrons occurs because an electron that is delocalized over a larger molecule has a smaller probability to tunnel out into the contacts. By comparing wires of different lengths, we can observe that the longer wires display not only sharper peaks in their LDOS but also a larger number of peaks. In addition, the HOMO–LUMO gap continuously gets smaller when going from a 1-ring to a 4-ring OPV (not shown in the figure) but converges to a given value for the longer wires of Fig. 1.2. Such effect is related to the negligible effects that contacts play the longer the wire becomes. The coherent current flowing through a molecule can be calculated from Landauer formula [30] by integrating the transmission function T(E) in the energy

Fig. 1.2 Local DOS of four different unfunctionalized OPV molecules. The Fermi level (Ef0) of the gold contacts at equilibrium is also shown. From: [59] Copyright Wiley-VCH Verlag GmbH & Co. KGaA. Reproduced with permission

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Fig. 1.3 Transmission probability of the OPV5 unfunctionalized as a function of energy for different applied voltages V. Ef0 denotes the equilibrium Fermi level of the electrodes. For better clarity, the non-equilibrium transmission functions have been vertically shifted for rising bias voltages. One vertical step corresponds to a difference in applied bias of 0.20 V. The vertical line represents the location of the constant Fermi level Ef0 of one contact, while the Fermi energy of the other contact Ef0 − eV is visualized by the tilted line. From: [59] Copyright Wiley-VCH Verlag GmbH & Co. KGaA. Reproduced with permission

range created by the voltage applied between the two electrodes. A typical example of the bias dependence of the transmission function is shown in Fig. 1.3. There we see that the peaks in the transmission functions exhibit a change in height, form, and relative position as a function of bias. In particular the amplitude of the transmission peaks decreases for increasing voltages. The reason is that an applied bias voltage at the contacts leads to an additional potential drop over the molecule, which in turn enhances the localization of the electronic states on the molecule. Since state delocalization is the prerequisite for these states to act as a channel for electronic transport, the applied voltage results in diminished transmission probabilities through these states. For longer molecules, the lowering of the transmission peaks for applied biases is even stronger. In such regime, the electrons go from one contact to the other only by “hopping” from one localized state to another, with a reduced transmission probability. The linear potential drop is also responsible for the shifting of the transmission peaks toward lower energy values. Figure 1.4 compares the I–V characteristics of the four OPV5–OPV8 unfunctionalized wires. All structures display higher currents in the resonance regime as opposed to the tunneling one. The threshold voltage does not vary significantly as the transmission gap for such wires is relatively constant. The current decreases as a function of wire length. The threshold behavior in the current characteristics is a

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Fig. 1.4 Current–voltage characteristics for OPV5–OPV8. From: [59] Copyright Wiley-VCH Verlag GmbH & Co. KGaA. Reproduced with permission

consequence of the transmission gap. Examination of Fig. 1.3 clarifies that, as long as the bias window only comprises energies with negligible transmission probabilities, the current remains low and stems from tunneling. At sufficiently high bias, the current starts increasing due to the resonances appearing in the window (around 1.4 V for the OPV5). Plateaus appear in the I–V curve at higher bias (as for instance around 2 V for the OPV5), due to decrease of the transmission peak connected to the conducting states as the voltage increases. As soon as a new resonance is available for conductance, the current increases again. Despite the capability of theoretical approaches like gDFTB to model transport in single molecules, such tools can only be applied to molecular systems with a limited number of atoms. Furthermore, the metal contacts need to be greatly simplified. Thus, in order to model realistic molecular devices, where dissipation and parasitic effects play a fundamental role, different approaches have to be followed. One possibility that will be discussed below is to develop an equivalent circuit description of the molecular element and to use SPICE-like approaches to model complex molecular systems. Such equivalent circuit can originate either from an atomistic calculation as provided by gDFTB or directly from experimental results.

Power Dissipation in Molecular Junctions So far, transport in single molecules has been treated completely ballistic, that is neglecting scattering and dissipation phenomena. In reality, molecules possess their own motion (in the form, e.g., of vibrational or rotational degrees of freedom) which causes interaction processes with the charge carriers moving across. In this part, we illustrate how to take such interactions into account and what effect scattering has in molecular transport [61]. The usual procedure to treat molecular vibrations is to

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expand the effective nuclear potential up to the harmonic term and to decouple the Hamiltonian as a superposition of independent one-dimensional oscillators corresponding to the normal modes of vibrations. Each vibrational mode will be labeled by q. The harmonic oscillators can be quantized following the usual prescriptions, by making use of the standard relationships between the position operator and the Bose field operator. The calculation of the electron–phonon scattering requires an explicit evaluation of the electron–vibration couplings matrices, obtained by expanding the TB Hamiltonian to first order in the atomic displacements [48, 62]. The electron–phonon interaction is treated within perturbation theory of the nonequilibrium Green’s function formalism and the current through the junction is computed by the Meir–Wingreen formula using the appropriate self-energies for electrons and holes [63]. The thermally averaged phonon population, Nq , can be obtained to first approximation by the Bose–Einstein distribution function, using the environment temperature. A more sophisticated calculation requires a self-consistent calculation of such a distribution as a function of applied bias, as discussed in the next section. The electron–phonon interactions can be viewed as an exchange of particle with a virtual contact [30] which adsorbs electrons at a given energy and emits them at another energy, accounting for the energy loss in the phonon quanta. In perfect analogy to the real contacts, the virtual contact brakes the phase coherence of the wavefunction. The amount of power dissipated in the molecule, due to inelastic phonon emission, can be obtained by considering the virtual contact current, as discussed for instance in [48, 30]. The power dissipated is given by the net rate of energy transferred to the molecule and can be calculated using the virtual contact current. The power dissipated can then be used to compute the rate of phonon emission. In order to compute the non-equilibrium phonon population under bias, a phenomenological rate equation is used. The rate of phonon emission can be defined   as Rq Nq = Wq /ωq , representing the ratio between the energy emitted per unit time in the oscillator q divided by its energy. This is generally a function of bias and depends on the phonon population itself. The rate Rq is actually the net rate of phonon emission, also including the absorption rate due to assisted tunneling and electron–hole pair production, very important in metal contacts. In order to compute the phonon population of the vibrational modes a rate equation can be written, including the rate of emission and dissipation into the leads, as   dNq   Rq Nq − Jq Nq − Nq0 (T) , dt

(1.5)

balancing the rate of quanta emitted with the rate of phonon decay to the bath, Jq , discussed below. This tends to restore the equilibrium Bose–Einstein distribution, characterized by the contact temperature, T. Under stationary condition the  phonon distribution on the molecule is given by Nq = Nq0 (T) + Rq Nq /Jq . The phonon dissipation rate is by no means a simple quantity to be predicted from first-principles calculations, since a large number of different mechanisms participate in phonon relaxations. For this reason Jq can be regarded in many cases as a fitting parameter of the model. Nonetheless we compute an upper bound of this

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Molecular Electronics: Challenges and Perspectives

11

Fig. 1.5 Representation of the system simulated comprising a styrene molecule adsorbed on a Si(100) 2 × 1 substrate. From: [61] Copyright 2007 by Taylor & Francis Group, LLC

parameter by considering the elastic coupling of the molecular modes with the contact vibrations. We consider as example the hybrid system shown in Fig. 1.5, comprising a Si(100) substrate, reconstructed 2×1, with an adsorbed styrene molecule in a bridge position and an Ag metal contact which models an STM tip. The position of the tip was chosen in order to obtain a relatively large direct coupling between the tip and the π orbitals of the styrene which guarantees a sufficiently high conductance. The figure shows a unit cell of the system considered, but periodic boundary conditions have been imposed. The Si substrate is heavily p-doped in order to make it conducting and the Fermi level is assumed at the valence band edge. While electrons cross the molecule, they interact with the molecular ionic vibrations from which they can be inelastically scattered. The electron–phonon scattering within the leads is not considered. In order to study the electron–vibron coupling we first relax very accurately the structure (this is done under no applied bias). Then we compute the vibrations of the molecule constraining the Si and Ag atoms. In order to calculate the rate of phonon dissipation into the contacts the molecular modes are coupled with the bulk vibrations. Such a calculation is performed using a Green’s function approach similar in concept to the electronic calculation. This formulation is possible because the atomic coupling, expressed by the dynamical matrix, is restricted to few neighbors. The imaginary part of the self-energy is used to extract the vibron lifetime. This approach includes first-order one phonon to one phonon decay processes, but obviously neglects many other mechanisms that may take place when the direct decay is not allowed by energy conservation. This happens, for instance, to the high-frequency modes, characteristic of molecular vibrations, generally lying well beyond the vibrational bandwidth of the bulk reservoirs which cannot decay other than via one-to-many phonon channels. Other decay mechanisms may involve coupling with the surrounding molecules and generally depend on the environment or multistep processes and anharmonic couplings. The result of this calculation is shown in Fig. 1.6, reporting the superposition of the phonon density of states of the coupled system (gray area) with the uncoupled

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Fig. 1.6 Vibrational density of states of the system Si–styrene–Ag. Gray area represents the Si DOS, vertical lines the uncoupled molecular modes, and solid line the DOS projected on the molecular modes showing their broadening due to coupling with the substrate. From: [61] Copyright 2007 by Taylor & Francis Group, LLC

molecular frequencies shown as vertical dashed lines. The cut-off frequency of the Si vibrations at 500 cm−1 clearly appears in this plot. The solid line represents the projected density of states obtained by approximating the self-energies just as a broadening and frequency shift. As discussed above, the calculation gives realistic results for those molecular modes lying within the Si phonon bands, where the broadening is sizable. The corresponding phonon decay rates are in the range 1011 − 1012 Hz. For those energy modes lying beyond the contact bandwidth the broadening sharply decreases, leading to decay rates as slow as 102 Hz for the highest modes, which is rather unrealistic. Therefore, the lowest limit for the decay rate has been fixed to Jq,min = 106 Hz, in all subsequent calculations. We find that the out-of-equilibrium phonon population is strongly bias dependent. Figure 1.7 reports the behavior of the average molecular temperature as a function of applied bias for two different contact temperatures (10 K and 300 K). The molecular temperature, Tmol , is computed by setting the energy balance expressed with  q

ωq Nq =



ωq nq (Tmol )

(1.6)

q

where nq (Tmol ) is the Bose–Einstein distribution for the temperature Tmol . As the bias increases, the temperature rises since more heat is dissipated in the molecular vibrations. The figure reports three different calculations obtained for different

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13

Fig. 1.7 Molecular temperature as a function of applied bias for different types of approximations in the electron–phonon couplings (see text). From: [61] Copyright 2007 by Taylor & Francis Group, LLC

approximations in the treatment of the electron–phonon coupling. The dotted lines correspond to the simplest lowest order calculation of the electron–phonon selfenergy, not including the renormalization of the electron propagator; the dashed line corresponds to the first-order correction, commonly known as first-order Born approximation (BA), including renormalizations of the propagator to first order. The solid line corresponds to the self-consistent Born approximation (SCBA) where self-energy and propagator are computed self-consistently. We can conclude that, because of the small incoherent tunneling current, the inclusion of higher orders in the electron-phonon coupling brings only small corrections to the final result. In Fig. 1.7 it is possible to appreciate the change in slope at the applied bias of 1.0 V. The total tunneling current at this bias is 1.2 nA. The origin of this effect comes from a molecular resonant state entering the injection window at the applied bias of 0.95 V. This has the effect of strongly increasing the coherent and incoherent currents. On average all vibrational modes are excited as the bias increases, although some of them are particularly favored, such as the lowest vibrational mode, at the frequency of 10.55 cm−1 , corresponding to a rigid oscillation of the whole benzene ring, away and toward the Ag tip. This mode leads to a strong variation of the molecule–metal matrix elements and, therefore, to a large electron–phonon coupling. Once the first resonance is reached, most of the phonon emission occurs into the lowest energy mode, leading to a sharp increase of molecular temperature.

Perspectives The conduction observed in single molecules connected to electrodes opens the way for a variety of electronic applications, rectification being one of the first properties that researchers tried to study for molecular devices, with the first investigations dating back to 1974 [10]. One example is given in [64], where a molecular rod that consists of two weakly coupled electronic π -systems with mutually shifted energy levels is realized. There, the resulting asymmetry manifests itself in a

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current–voltage characteristic which depends on the sign of the bias voltage like in a conventional diode. Other studies on the rectification properties of molecules can be found in [65] and [66], where a the oretical view is also offered. Adding a third electrode to obtain transistor action has been proven difficult so far, and the roadmap toward the development of single molecule transistor is just at the beginning [67]. In 1998, Sander et al. [68] reported a field effect transistor working at room temperature, using a carbon nanotube as semiconductor. In 2009 Song et al. [69] realized a solid-state molecular device, in which transport current is directly modulated by an external gate voltage, which changes the energy of the molecular orbital. A further application of single-molecule devices is as active element of a memory, because they can be intrinsically good hysteretic switches and exhibit highly nonlinear current–voltage characteristics [70]. For the above reasons it seems promising to exploit special circuit architectures, like crossbar memories, which have a very simple and regular geometry and which are built exclusively from two-terminal switches and nonlinear elements [71–73]. Next we will describe the properties of these particular molecular devices.

Crossbar Memories Crossbar passive memories [71, 33] are probably the simplest functional electrical circuits. They are built from horizontal and vertical conducting wires where a switching element is placed at each wire crossing. If the switches are made from molecular monolayers, then the size of the storage elements can be scaled down to molecular dimensions, e.g., in the few nanometer regime. Some nanofabrication methods (such as nanoimprint lithography) may enable the fabrication of the contact wires on a similar size scale [74]. For this reason, molecular crossbar memories received a lot of attention recently and there is a number of experimental [71] and theoretical [75–78] publications devoted to their study. Logic devices can also be built using similar principles [72]. In this work we assume that the read-out and write in circuitry of the memory (i.e., multiplexers/decoders) are realized with (standard) silicon technologies and only the storage array is molecular-based. A molecular crossbar memory circuit should be integrable with conventional silicon microtechnologies and would require the introduction of additional fabrication steps [79–81]. Only a relatively large-scale molecular memory would make such technology transition to pay off: if the size of the molecular memory banks is too small, the silicon-based interface circuitry occupies most of the chip area. Crossbar memories are passive circuits and they contain no amplifying/signal-restoring elements. This can severely limit their scalability, and parasitic current paths can interfere with the read-out process. In this section, we investigate molecular crossbar memories from a circuit design point of view. We will investigate what properties the molecular I(V) curve should have in order to be a useful element of a scalable crossbar memory and we will show that “real” molecules exactly show such thresholding-type nonlinearities. The sketch of a crossbar circuit is shown in Fig. 1.8a. It is built from horizontal and

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Molecular Electronics: Challenges and Perspectives

15

Fig. 1.8 Physical layout of the molecular crossbar (a) and a cellular model for the simulation of the circuit (b). From: [33] Reproduced with permission. Copyright 2009 IEEE

vertical conducting wires and at each wire crossing a switching element is placed. The circuit representation of the array is sketched in Fig. 1.8. The junction can have two distinct states, the on and the off states, corresponding, respectively, to a low R = Ron and a high R = Roff resistance, which depends on the history of the junction. This is modeled by setting the switch of Fig. 1.8b to the on or off position. The series resistance of the interconnecting wires is also included in Fig. 1.8; however, the small (couple of tens of ohms) resistance of metallic interconnections is negligible compared to the typically several megaohms resistance of molecular junctions. We allow the junction resistances to be nonlinear (i.e., function of the applied voltage). To get a qualitative picture of the crossbar operation, we consider junctions with linear I(V) characteristics and zero serial resistances. The most straightforward readout scheme [71] biases the interrogated junction and measures the current flowing from the junction toward the ground, as illustrated in Fig. 1.9a. All the unselected bit and word lines are put to ground. The schematics of a read-out circuitry (i.e., a resistor and a comparator) are also shown. By redrawing the circuit in the way it is illustrated in Fig. 1.9b, it is apparent that the current or sense voltage is influenced only by the resistances connected to the same bit line as the interrogated bit. They are connected in parallel to Rsens , effectively changing its value. It is clear from this circuit model that the parasitic resistances connected to the same bit line pull down the sensing voltage. Very small values of Rsens are required to maintain a reasonably large noise margin. Sense resistances in the kiloohm regime

16

Vdd

Rn Rn–1 Rn–2

…

Fig. 1.9 Resistor model of the crossbar circuitry. a the resistance state of Rn is probed. b a simplified circuit diagram, with the resistances that influence the value of ibit /Vsense. The sense current is measured as a voltage drop on Rsens and fed into a comparator. From: [33] Reproduced with permission. Copyright 2009 IEEE

P. Lugli et al.

R1 Rsens

Vref

a) Rn

Vdd

Vsens

b)

Rn–2

R1

Rsens

…

Rn–1

or below become increasingly difficult to realize if one takes into account the resistance of the wires that connect the nanoscale crossbar array to a silicon-based read-out circuitry. Another disadvantage of this read-out method is that it drives a current through a large number of unaccessed junctions thus dissipating power unnecessarily—unless the bit values along this word line are read out in parallel. The frequent access may cause early degradation of the molecular junctions and the driven word line is loaded with a very high current, potentially destroying it. The “wasted” current and power are proportional to the size of the array n. Another possible read-out scenario involves leaving the unselected bit and/or word lines floating. This minimizes power dissipation and current inflow. Unfortunately in that case the parasitic current paths no longer end in a shortcut to the ground, but they flow into the signal path and interfere with the read-out process. In a realistic case a crossbar memory is built from nonlinear, non-rectifying elements, such as the molecules investigated in [70]. We assume a self-assembled monolayer built from 100 molecules with each molecule having the same current– voltage characteristics as a stand-alone molecule in the break-junction experiment of [70]. Our choice is a rough estimation for the number of molecules in a selfassembled monolayer, covering few tens of nanometer squared area junction. The static I(V) curve of the molecules (i.e., the two branches of the hysteretic switch) was implemented by piecewise linear voltage-controlled current sources in SPICE, as shown in Fig. 1.10. This example also serves as a model system for a large class of realizable molecular switches. We assumed a symmetric I(V) curve (I(V0 ) = I(−V0 )), even if the real molecular I(V) is slightly asymmetrical. The figure also shows the current corresponding to Ron = 3.5 M and Roff = 23 M values that we used in the linear model. When the junction is biased to

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Molecular Electronics: Challenges and Perspectives

Fig. 1.10 The I(V) curve of the investigated molecular monolayer, based on [70]. From: [33]. Reproduced with permission. Copyright 2009 IEEE

17

I [nA] 350 nA ON Ron = 3.5 MW

OFF Roff = 23 MW

0 0

0.7V

V [V]

1.5 V

V = 0.7 V, the currents flowing through the “real” molecular layer and these resistors is the same, which allows us to compare our results with (linear) resistive and nonlinear junctions and understand the benefits or disadvantages of nonlinearities. The scalability diagram (relative noise margin) of the crossbar is shown in Fig. 1.11. For 100 × 100 arrays the read-out margin for floating junctions is about 10 times larger with the nonlinear junctions. The voltage of the word lines stabilizes slightly below Vdd /2 and the bit lines are settled a bit above Vdd /2. The unselected junctions get about half of the voltage of the selected junction and due to the steep nonlinearity only very small current flows on them. The finite parallel resistance of molecular junctions still results in a “background” current, making the read-out more difficult at larger array sizes. From Fig. 1.11 we can extrapolate though that noise margin will not be a crucial problem up to many hundred kilobit arrays. The dashed curve of Fig. 1.11 shows the relative noise margin if all the unselected junctions are biased to V0 = 0.1 V—biasing significantly improves the noise margin but it will also increase dissipation and unnecessary current inflow. For the 100 × 100 array the current inflow in the biased word line is only three times bigger than the sense current on the interrogated bit line. It is clearly possible to find a good compromise between the read-out margin and the extra current inflow/power. 1 Ion – Ioff 2 Ion Ioff

Fig. 1.11 Scalability of the crossbar with non-linear junctions if the unselected wires are left floating or they biased to a V0 = 0.1 V voltage. From: [33]. Reproduced with permission. Copyright 2009 IEEE

Relative noise margin

0.35 0.3 V 0 = 0.1 V

0.25 0.2 0.15 0.1 Floating junctions

0.05 0

10 20 30 40 50 60 70 80 90 100 Array size

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P. Lugli et al. on

Vthreshold

V in

I

V

off Vthreshold

V0

V0

V in

Fig. 1.12 Current–voltage characteristics of an idealized molecular switch and its corresponding read-out scheme. From: [33] Reproduced with permission. Copyright 2009 IEEE

on off An ideal, step-like nonlinearity with distinct Vthreshold and Vthreshold voltages (see Fig. 1.12) in the current–voltage characteristics of the molecule clearly would elimoff − inate the problems of read-out. Biasing the chosen word line to V in = (Vthreshold on Vthreshold )/2, grounding the selected bitline, and putting all the unselected connecoff on tions to V 0 = (Vthreshold − Vthreshold )/4 voltage, the parasitic currents cease, as long on 0 as V < Vthreshold . For non-ideal step-like nonlinearities the leakage currents below the threshold voltage add up, resulting in a background current. This eventually reduces the noise margin, as shown in Fig. 1.11.

Organic Thin-Film Transistors In was the year 1977, when Alan J. Heeger, Alan G. MacDiarmid, and Hideki Shirakawa discovered a carbon-based, highly conductive polymer: the oxidized, iodine-doped polyacetylene. For their discovery, which was one of the most important milestones for organic electronics, they were jointly awarded the chemistry Nobel Prize in 2000. Since then, carbon-based semiconductors have allowed scientists and engineers to develop devices with novel features and reduced costs, making this technology a premier candidate for several sectors of electronics. Organic semiconductors can be manufactured and processed at room temperature, making their production easier and cheaper than for conventional silicon and inorganic semiconductors; they can be transparent, flexible, and developed over large areas or non-planar geometries; completely plastic devices can be realized. Their performances, compared to silicon, are, however, inferior: carrier mobility is orders of magnitude lower, even if this largely increased in the last years; they are highly sensitive to environmental conditions, especially to the atmosphere (oxygen and humidity); their performances decrease over time. Despite these drawbacks, the great potential of organic electronics has led to extensive theoretical and experimental research since the first discoveries during the late 1970s. Organic transistors are three terminal devices in which the current flow going between the source and drain is modulated by a gate potential. A major difference

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Molecular Electronics: Challenges and Perspectives

Fig. 1.13 Structure of a top contact transistor

19

Source

Drain Semiconductor Insulator Gate Substrate

Fig. 1.14 Structure of a bottom contact transistor

Source

Semiconductor

Drain

Insulator Gate Substrate

with commonly used inorganic transistors is that no inversion layer is formed, but the conduction occurs by means of the majority carriers, which accumulate at the semiconductor/insulator interface. Possible transistor structures are shown in Figs. 1.13 and 1.14. Both have a substrate which acts as mechanical support for the structure. Over it, there is an insulating dielectric film, under which a gate contact is realized. Top contact structures have the semiconducting layer all over the insulator, with the source and drain contacts lying on top of the semiconductor; on the contrary, bottom contact devices have their contacts under the semiconductor layer. Moreover, both structures can also be realized without the substrate, if the mechanical support to the structure is provided by the insulating film itself (free standing devices). In this section we will analyze organic transistors and simple circuits that can be realized with them, like inverters and ring oscillators. We will describe the structure and physical behavior of the transistors, as well as their electrical characteristics and associated models. Since the physics of organic semiconductors is quite different from that of silicon, because of their molecular structure, we will first describe how charge transport occurs inside the semiconductor.

Charge Transport in Conjugated Polymers Materials employed as organic semiconductors are conjugated polymers, i.e., sp2 hybridized linear carbon chains. This kind of hybridization is the one responsible for giving (semi)-conducting properties to organic materials. Starting from the electron configuration of a single carbon atom, which is 1s2 2s2 2p2 , when multiple carbons bond together different molecular orbitals originate, as the electron wavefunctions mix together [82, 83]. While 1s orbitals of the carbons do not change when the atoms are bonded, 2s orbitals mix their wavefunctions with two of the three 2p orbitals, leading to the

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P. Lugli et al.

Fig. 1.15 sp2 hybridization of two carbon atoms. sp2 orbitals lie on the same plane and bond into a σ bond, pz orbitals are orthogonal to the plane and bond into a π bond

electron configuration that is reported in Fig. 1.15. Three sp2 orbitals are formed and lie on the molecular plane, at 120◦ to each other, leaving one p orbital which is orthogonal to the molecular plane. Hybrid sp2 orbitals can then give origin to different bonds. sp2 orbitals from different carbon atoms which lie on the molecular plane form strong covalent bonds, which are called σ bond, whereas p orbitals which are orthogonal to the molecular plane can mix to give less strong covalent bonds, which are called π bonds. The π bonds constitute a delocalized electron density above and below the molecular plane and are responsible for the conductivity of the molecule, as the charge carriers move through these bonds. This transport process is usually called hopping transport [84, 85] and is described by means of quantum mechanical tunneling. The energy levels of the orbitals, when multiple molecules are considered, give origin to energy bands, in analogy to what happens in inorganic semiconductors: the edge of the valence band corresponds then to the highest occupied molecular orbital (HOMO), whereas the edge of the conduction band corresponds to the lowest unoccupied molecular orbital (LUMO). The difference between the energy of the HOMO and the energy of the LUMO is the energy gap Eg of the organic material and usually 1.5 < Eg < 4 eV [86]. Charge transport in organic semiconductor is, however, quite different with respect to silicon and other mono-crystalline inorganic semiconductors. The periodic lattice of these materials and their very low density of defects allow one to accurately describe the charge transport by means of delocalized energy bands separated by an energy gap. Most of the organic semiconductors, on the other hand, are amorphous and rich in structural and chemical defects, therefore requiring conventional models for charge transport to be adapted and extended; moreover, charges can move, with different mobilities, within the molecular chain (intrachain), between adjacent molecules (inter-chain), or between different domains, generally referred to as grains (inter-grain). In reality, transport in organic semiconductors is a much more complex process than described above [87]. One possible description can be obtained in terms of

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21

hopping processes along molecular chains and controlled by quantum mechanical tunneling. In the following, we will describe a simplified approach similar to those used in inorganic semiconductors. Hopping transport has been simulated with the Monte Carlo method: analysis of the temperature and electric field dependence of the mobility can be found in [88], and later in [89, 90], where the dependence on the temperature and the electric field of the carrier mobility is studied; in [91] Olivier et al. study the impact of the molecular parameters on hopping rates and charge mobilities in organic π -conjugated materials.

Drift Diffusion Model Simulations for organic devices and more complex structures, which thoroughly account for the hopping theory, can be too complex and computationally onerous, so simpler models have been adapted from the physics of the inorganic semiconductors. One of the most widely used models for semiconductor simulations is the drift diffusion model, which consists of a set of nonlinear partial differential equations that relate three physical quantities, namely the electrostatic potential V, the density of electrons n, and the density of holes p inside the device structure. The first of these equations is the Poisson equation: ∇ · (ε∇V) = q (n − p + NA − ND + ntr ) ,

(1.7)

where ε is the electric permittivity of the material; q is the elemental charge; NA and ND are the concentrations of ionized acceptors and donors, respectively; and ntr is the density of occupied traps. The continuity equations are ∂n , ∂t ∂p ∇ · Jp = −qRp − q , ∂t ∇ · Jn = +qRn + q

(1.8) (1.9)

where Jn and Jp are the current densities and Rn and Rp are the net generation– recombination rate. In the DD model the currents of electrons and holes are described as the sum of two contributions, namely a drift component, proportional to the electrostatic field E = −∇V, and a diffusion component, proportional to the gradient of the carrier density. Jn = −qnμn ∇V + qDn ∇n,

(1.10)

Jp = −qpμp ∇V − qDp ∇

(1.11)

The charge transport properties are described using the mobilities μn and μp and the correspondent diffusivities Dn and Dp , which are assumed to be related by the Einstein relation D = kT/qμ. As already mentioned previously, they can

22

P. Lugli et al. Table 1.1 Mobility of p-type and n-type semiconductors Mobility (cm2 /Vs)

Compound p-Type Pentacene Picene 2,7-Diphenyl[1]benzothieno[3,2-b]benzothiophene DNSS Rubrene (single crystal) Bis-5‘-alkylthiophen-2‘-yl-2,6-anthracene Thiophene oligomers Phenylene systems n-Type Perlylenediimides Fullerene Perfluoronated pentacene Thiophene oligomers with perfluorohexyl groups

3.0 1.1 2.0 2.9 15 0.5 1.1 0.32 0.6 0.56 0.11 0.048

be field-and temperature-dependent. Table 1.1 shows the highest (so far) measured mobilities for some organic p and n semiconductors. Reference [92] contains a complete and in-depth review of organic semiconductor mobility. The density of carriers can be described by means of Boltzmann statistics: 

 EqF,n − EC n = NC exp , kT   EV − EqF,p p = NV exp , kT

(1.12) (1.13)

where EqF,n = −qn and EqF,p = −qp are the quasi-Fermi energies for electrons and holes and n and p are the quasi-Fermi potentials, respectively. NC and NV are the effective densities of states and are usually assumed to be equal to the density of molecules, since all the states are thermally accessible [93]. EC and EV are the conduction and valence band edges, defined as EC = −qχ − q (V − φref ) ,

(1.14)

EV = −qχ − Eg − q (V − φref ) ,

(1.15)

where qχ is the electron affinity and Eg the band gap. The reference potential φref can be set equal to the Fermi potential of an intrinsic semiconductor. Then Eqs. (1.12) and (1.13) become q (V − φn ) , (1.16) n = ni exp kT   q φp − V p = ni exp , (1.17) kT   √ where ni = NC NV exp −Eg /2kT is the intrinsic density.

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Molecular Electronics: Challenges and Perspectives

Fig. 1.16 Band diagram for a Schottky contact between an n-type semiconductor and metal at the thermal equilibrium. qφ s is the workfunction of the semiconductor, EC is the conduction band level (LUMO in organic semiconductors), EV is the valence band level (HOMO)

23

Vacuum level q q m

q s q B

EF

q ms

EC EF

EV

Boundary conditions are required to solve the DD equations for the device structure. If a metal/semiconductor interface is present, it has to be specified whether it constitutes an ohmic or Schottky contact, as well as for metal/insulator interfaces (e.g., a gate contact in a transistor). For ohmic contacts charge neutrality and equilibrium are assumed at the metals/semiconductor interface. For Schottky contacts, a barrier height is considered (the difference between the metal workfunction qφ m and the electron affinity qχ ), given by the difference qB = qφm − qχ , as reported in Fig. 1.16, which shows a band diagram for a Schottky contact between an n-type semiconductor and metal, including also the difference between the metal and the semiconductor workfunction qφms .

Analytical Models for OTFTs The determination, by analytical means, of the drain current for any applied voltages has been object of extensive research over the years. In this section, we will describe a model based on constant mobility and doping, in linear and saturation region. It is mostly based on [94]. Extensions of this model, accounting for space charge limited currents and Poole–Frenkel mobility can be found in [95]. Other contributions to the modeling of the organic transistors, including the effects of traps and ambipolar devices, come from Stallinga et al. in [96, 97]. Figure 1.17 shows the basilar structure for the transistor to be modeled. It is a free-standing bottom contact structure. The length of the channel is L, its width is Z. The dielectric layer has thickness di and dielectric permittivity εi , with an associated capacity Ci = εi /di , whereas the semiconductor film has thickness ds and dielectric permittivity εs , with an associated capacity Cs = εs /ds . We will assume an n-type semiconductor with doping N and a density of free carriers n0 N; an analogous model can be derived for p-type semiconductors changing the sign of the current and the applied voltages.

24

P. Lugli et al. L

y ds Source 0

Semiconductor dx

di

Drain

Insulator Gate

Fig. 1.17 Geometry of the bottom contact transistor

The threshold voltage of the device, which accounts for different workfunctions between the semiconductor and the gate and for possible charges located in the insulator or in the insulator/semiconductor interface, is set to be zero, to simplify notation. Since it just determines a shift of the gate voltages, non-zero threshold voltages can be included in the model substituting Vg with Vg − Vth . The total drain current Id in the linear region (Vd < Vg ) can be expressed as the sum of the bulk current originating from the free carriers in the semiconductor and the current determined by the carriers in the accumulation layer. Therefore

dV Id = − Qg (x) + Q0 , Zμ dx

(1.18)

where Q0 = qn0 ds is the surface density of the free carriers and

Qg (x) = −Ci Vg − Vs (x) − V(x) is the surface density of the carriers in the accumulation layer, which forms as a capacitive effect. Vs (x) is the ohmic drop in the bulk of the semiconductor, which can be generally neglected [98], and V(x) is the potential with respect to the source at the coordinate x. Equation Eq.(1.18) can be integrated from V(x = 0) = 0 V to V(x = L) = Vd to obtain, for a constant mobility,

  Vd2 Z . Id = μCi Vg + V0 Vd − L 2

(1.19)

The transconductance in the linear zone, from which the field effect mobility can be extracted, can then be defined as  gm =

∂Id ∂Vg

 Vd =const

=

Z μCi Vd . L

(1.20)

When the drain voltage exceeds the effective gate voltage Vd > Vg the accumulation layer near the drain changes to a depletion layer. The depletion layer will extend from a coordinate x0 such that V(x0 ) = Vg to the drain contact (x = L). At those coordinates where there is the depletion layer, the only contribution to the current is

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Molecular Electronics: Challenges and Perspectives

25

given by the free carriers, which are only in the volume of the semiconductor which has not been depleted. Then Id dx = Zqμn0 [ds − W(x)] dV,

(1.21)

wherein W(x) is the width of the depletion region, which can be determined solving the Poisson equation [98] to get ⎫ ⎧

⎬ ⎨ 2 2Ci V(x) − Vg εs W(x) = 1+ −1 . ⎭ Ci ⎩ qNεs

(1.22)

Since we have assumed that the accumulation layer extends up to a point where V(x0 ) = Vg and since beyond x0 only the non-depleted free carriers add to the current, we can write the latter as the sum of these two contributions: Id =

Z μCi L



Vg 0

  Z Vg + V0 − V dV + μqn0 L



Vdsat

(ds − W) dV.

(1.23)

Vg

The second integral on the right-hand side means that we account for all the free carriers which are in the semiconductor out-of-the-depletion region, whose extension is W(Vg ) = 0 at the end of the accumulation layer and is W(Vdsat ) = ds when the device reaches the saturation voltage. Changing the integration variable in Eq. (1.23) from V to W leads to Id = =

 Vg Z i 0 L μC   Z Lμ

Ci

  d 2 Vg + V0 − V dV + ZL μ q εns0 N 0 s (ds − W) W +    Vg2 q2 n0 N ds3 3Cs + 1 + + V V , 0 g 2 εs 6 Ci 

εs Ci



dW =

(1.24) The pinch-off voltage Vp , i.e., the gate voltage for which the depletion region extension is equal to ds , can be obtained by substituting Vp = Vg − V(x) in Eq. (1.22). This leads to   Cs qNds qNds2 Vp = ± 1+2

, (1.25) 2εs Ci Ci wherein in the approximated expression the flat band voltage has been neglected and ds  di is reasonably assumed. If n0 = N is also assumed, then Vp = V0 and  2 Z (1.26) μCi Vg − V0 . 2L Figure 1.18 shows a simulation of OTFT output curves based on Eqs. 1.19 and 1.26. In the previous calculations, the mobility has always been considered constant; however, this assumption is rather simplistic, as it usually depends on the temperature and the electric field in the semiconductor. Common models are the Idsat =

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0

x 10−5

Id (V)

−0.5

−1 Vg = −20V Vg = −40V Vg = −60V Vg = −80V −1.5 −100

−80

−60

−40

−20

0

Vd (V)

Fig. 1.18 Output curves simulated with Eq. (1.19) and (1.26). Z/L = 200, μ = 10−3 cm2 /s, Ci = 2.3 · 10−8 F/cm2 , V0 = −1V

multiple trap and release (MTR) mobility model [99] or the variable range hopping (VRH) [100], for which the effective mobility is μFET =

 α ∂I L = μ0 Vg − Vth , Ci WVd ∂Vg

(1.27)

wherein Vg is the applied gate voltage and μ0 and α are parameters usually extracted by means of fitting of the experimental data. Another mobility model was theorized in 1938 by Frenkel [101], to explain the increase of conductivity in insulators and semiconductors when high fields are applied. Its form is  √  μ = μ0 exp γ E , (1.28) where μ0 and γ are parameters which depend on the physics of the considered system and E is the electric field. Poole–Frenkel mobility has been extensively studied for modeling charge transport in organic LEDs with disordered semiconductors [102–104], but it can also describe several experimental results for organic field effect transistors which show a variation of the mobility with the source-drain electric field [105–107].

Simulation of Organic Thin Film Transistors We simulate an organic, bottom contact, thin-film transistor. The equations of the drift diffusion model are solved using the finite elements method [108]. The Poisson equation, together with the continuity equations, is solved as a system of partial

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Gate

Drain

Source

di

ds

L Fig. 1.19 Device mesh

differential equations on a discrete mesh grid. The solution is determined for each node of the grid. Figure 1.19 shows a possible grid for a device with channel length L = 50μm, channel width W = 5mm, semiconductor thickness ds = 30nm, and insulator thickness ds = 100nm. Even if it is not shown in the picture, air over the device is also simulated, because the electric field exceeds the semiconductor boundaries. The complete set of parameters used in the simulations is shown in Table 1.2. The output curves are shown in Fig. 1.20. For a deeper understanding of the device behavior, one can look at the potential or charge profiles inside the structure. For example, from Fig. 1.21 one can see how the potential in the semiconductor follows the gradual channel approximation, whereas the charge profile in Fig. 1.22 shows how, under the application of the gate bias, an accumulation layer of holes forms (and respectively, there is a depletion of electrons).

Table 1.2 Material parameters used in the simulation Parameter

Symbol

Value

Dielectric permittivity Semiconductor permittivity Electron affinity Energy gap Valence band density Conduction band density Electrons mobility Holes mobility Metal workfunction

εi εs qχ Eg NC NV μn μp qφ m

4 4 2.5 eV 2.5 eV 2.8 · 1021 cm−3 2.8 · 1021 cm−3 10−20 cm2 /Vs 0.0381cm2 /Vs 5 eV

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V_gs = −30V V_gs = −20V V_gs = −10V V_gs = 0V

Drain current (A)

−1e−07

−2e−07

−3e−07

−4e−07

−60

−40

−20

0

V_ds (V)

Fig. 1.20 Output curves for bottom contact OTFT device. Channel length is L = 50μm, channel width W = 5mm, semiconductor thickness ds = 30nm, insulator thickness ds = 100nm

Fig. 1.21 Potential distribution in the structure. Gate potential Vg = −30V, drain potential Vd = −35V

Experimental results in literature, for example the work of Schmechel and von Seggern [109, 110], show that the performances of organic transistors are usually affected by trap states located in the energy gap of the material. The origin of these localized states is still not completely clear: for example, shallow traps that can arise in vapor-deposited pentacene from the sliding of the molecules along the molecular axis, while two-dimensional crystallinity is

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Fig. 1.22 Net charge distribution in the semiconductor. Gate potential Vg = −30V, drain potential Vd = −35V

maintained [111]. Northrup et al. [112] discuss the effects of hydrogen-related defects in crystalline pentacene, i.e., when the pentacene molecule C22 H14 has one more hydrogen atom and becomes C22 H15 , but also analyze the effects of oxygenrelated defects, i.e., when one oxygen atom replaces one hydrogen atom to give C22 H13 O. Both defects originate on exposure of the semiconductor to air humidity, but hydrogen defects could also come from bias stress in the device. Water adsorption on the surface of the insulator has also been suggested for the generation of discrete traps states in single-crystal pentacene [113]. The theory of Schockley–Read–Hall [114, 115] can be applied also to organic semiconductor, including in the drift diffusion model exposed in section “Drift Diffusion model” one more equation that describes the trap dynamics:     1 1 dntr (Etr − Ei ) (Ei − Etr ) = ftr − n (1 − ftr ) + (1 − ftr ) − pftr , exp exp dt τn kT τp kT (1.29) where ntr = Ntr ftr is the density of occupied centers, proportional to the density of traps Ntr and to the probability of occupation ftr ; τn = 1/vth,n σn Ntr and τp = 1/vth,p σp Ntr are the lifetime for holes and electrons, respectively; vth,n , σ n , vth,p , σ p are the carrier thermal velocity and the capture section, for electrons and holes, respectively. Etr − Ei is the difference between the energy levels of the trap center and the intrinsic semiconductor. Figure 1.23 shows a simulation for a bottom contact transistor, in which the drain electrode has a constant bias Vd = −25V, while the gate electrode potential is swept between Vg = +40V and Vg = −40V, then again to Vg = +40V.

P. Lugli et al.

Drain Current (A)

30

-2e-06

-4e-06

–40

–20

0 Gate Voltage (V)

20

40

Fig. 1.23 Transient simulation of an organic transistor with W = 5mm, L = 75μm, di = 1.6μm, ds = 50nm. Acceptor traps at the interface have a surface density Ntrs = 1012 cm−2 , Etr = EV + 0.3eV, vth σn = vth σp = 2 · 1019 cm3 /s

The main macroscopic consequence of the presence of traps in a device is hysteresis [116, 117], because traps are charged and uncharged with specific dynamics which can lead to different operating conditions, even if the applied bias is the same. Initially, with a positive gate bias, the traps are filled with electrons, positively increasing the threshold voltage in the device. For Gauss’s law, the shift Vth in the threshold voltage is equal to Qtr (t) Vth = − . (1.30) Ci wherein Qtr is the surface-trapped charge and Ci the insulator capacitance. Once the gate potential becomes negative, holes are attracted at the interface and start to neutralize the negative charges, reducing the threshold voltage. If the trap charging and de-charging times are slow enough, a memory effect arises, resulting in a hysteresis. Analytical models [118], as well as numerical simulations [119, 120], have been proposed to study these phenomena, which still constitute a hot topic in the field of organic electronics.

Circuits Based on OTFTs: Inverters and Ring Oscillators A major restriction in the design of organic electronics results from the limitation to p-type transistors. Although research aims at realizing n-type devices [121], the respective material systems are still immature. Additionally, the patterning of nand p-type OTFTs on the same substrate poses great challenges in the fabrication processes. Therefore, it is of interest to design exclusively p-based circuits for digital

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Fig. 1.24 Inverter layout with two p-type OTFTs in (a) saturated and (b) depleted load configuration

and analog purposes [122]. Figure 1.24 shows two possible inverter layouts with depleted and saturated load. Generally, a great advantage of MOSFET-based circuits is the flexibility with which they can be tuned by adjusting the λ = W/L ratios. Figures 1.25 and 1.26 demonstrate the strong influence of the geometry factor =

Wdriver Lload λdriver = λload Ldriver Wload

on the inverter transfer characteristic. The depleted load circuit exhibits superior performance with respect to inverter gain and the matching of input and output voltage

Fig. 1.25 Influence of the geometry factor on voltage transfer characteristic of an organic inverter with saturated load

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Fig. 1.26 Influence of the geometry factor on voltage transfer characteristic of an organic inverter with depleted load

Fig. 1.27 Simulated voltage transfer characteristic of organic inverter with depleted load =17, gain of 4.6, and static noise margin of NML = VIL − VOL = −1.6V and NMH = VOH − VIH = −6.4V

ranges. An inverter with reasonable symmetry and gain is the one with =17 in Fig. 1.26. Figure 1.27 shows the associated transfer characteristics. It has a gain of 4.6 and a static noise margin of NML = VIL −VOL = −1.6V and NMH = VOH −VIH = −6.4V, respectively.

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Fig. 1.28 Response of inverter with depleted load (γ = 17) and a load capacity CL = 20fF to input pulse of T = 40μs. The upper panel shows the simulated output voltage transient and the lower panel the associated current consumption

To determine the switching behavior, we simulated this inverter in combination with a load capacity of CL = 20fF. The transients are plotted in Fig. 1.28. In practical circuit applications, CL is the sum of the input capacitance of the consecutive logic stage plus the parasitic capacitances of, for example, the wiring. The output voltage in Fig. 1.28 shows distinct asymmetry for rising and falling edges. The rise time going from 0 to −20V is approximately 5 μ s, while the fall time is close to 0.5 μ s. This asymmetry is a characteristic feature of inverters with depleted load and is also observed experimentally [123]. During the state Vin = 0V, the load capacitance CL is fully charged and Vout = −20V. Changing the input to −20V instantly opens the driver OTFT. The resulting current discharges the capacitance. When the driver OTFT is subsequently closed with Vin = 0V, CL needs to recharge in order to obtain the desired output level of −20V. For the charging process, current must flow through the load transistor, which still has a gate voltage of approximately 0 V. Therefore its impedance is initially high and the charging relatively slow. As demonstrated by the simulations, driving the output to −20V is as a result slower than shifting it in the opposite direction.

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The switching times depend on the magnitude of the load capacitance. The overall speed decreases with increasing CL . It is therefore important in the optimization of organic device and circuits to reduce unnecessary capacitances. Particularly critical are overlap capacitances at source and drain, which exist due to poor control on the positioning of the gate electrode. By inspecting the reported circuit layouts, it can be estimated that in terms of speed, most circuit realization are up to now rather limited by the layout than by the properties of the organic semiconductor. Current consumption is another critical circuit property. Non-complementary inverters have the disadvantage of constantly consuming power. The lower panel of Fig. 1.28 visualizes the supply current during pulse operation (T = 40μs). The switching of the input voltage causes strong peaks. But the invert also draws significant current from the supply, when the input is held at a constant level. The reduction of supply current is another interesting optimization task in which the presented simulation framework can fruitfully be employed. The realization of organic ring oscillators has been a key milestone [28, 124]. Operation frequencies of up to 220 kHz have been reported [125]. The great attention on these systems has resulted from the fact that for logic applications, it is not sufficient to simply build inverters. It is required that they amplify the input signal so that it is not lost after a number of stages. Furthermore the output of one logic stage must be able to drive the input of another one. This requires that input and output voltage ranges match. A ring oscillator consists of an odd number of inverter stages. The output of one stage is connected to the input of the next stage. The last inverter connects to the input of the first one closing the ring. The odd number of stages prevents that system from obtaining a stable operation point. What makes the oscillator particularly interesting is the fact that each inverter must obey all the previously mentioned requirements in order to allow persistent oscillation. The realization of ring oscillators has therefore been the proof that large integrated organic circuits are feasible. To test the capabilities of our simulation approach, we have set up a three-stage ring oscillator using the optimized inverter treated in the previous section. The overall circuit is shown in Fig. 1.29. We again included a load capacitance of Ci = 20fF

Fig. 1.29 Three-stage ring oscillator

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Fig. 1.30 Transient startup of oscillator circuit. Vdd is ramped to −20V during the first 0.5 μs

Fig. 1.31 Steady-state operation of simulated three-stage organic oscillator with Vdd = −20V

in each stage to explicitly account for parasitics. To start the oscillation, the supply voltage Vdd is ramped to −20V during the first 0.5 ms of the simulation. The node voltages at each inverter stage during startup are given in Fig. 1.30. After the initial Vdd ramp, the oscillator successfully reaches steady-state operation (compare Fig. 1.31). The simulated oscillation frequency equals 105 kHz and strongly depends on the magnitude of the load capacitances Ci . The stage delay, which results for the presented oscillator, has consequently a value of 3.16 ms. It is interesting to note that a half period of the oscillation is significantly shorter than the rise time of the transient inverter response in Fig. 1.28. Additionally, the output voltage range of the oscillator is limited to an interval of approximately −8 to −1V. Simulations have shown that the mismatch of rise and fall times in the inverter results in a timing deficiency within the oscillator. Effectively, the fast transmission of the falling signal in one inverter stage does not allow enough time for the slow rising edge in the following stage to reach a strongly negative value.

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In conclusion, we have shown that relatively complex circuits can be realized with organic transistors. Simulation is a valuable tool for the optimization of such circuits.

Perspectives The performances of organic semiconductor are continuously increasing, since their discovery in 1977. The mobility of the carriers has reached values comparable to those of the amorphous silicon, as shown by many promising compounds [92]. Integrated circuits have been developed; for example, ambipolar transistors and high gain inverters (output voltage gain as high as 30 V) have been reported 126, as well as unipolar inverters and multi-stage ring oscillator with single-stage delay of t = 712ns [127]. The IEEE Computer Society has already defined standard test procedures for the characterization of organic transistors and materials [128] and organic transistor-based ring oscillators [129]. Moreover novel architectures have emerged, setting the bases for new application fields: among the most promising, transistor-based sensors [130, 131], to detect chemical and biological species, organic RFID (Radio frequency IDentification) systems that can operate at 13.56 MHz at 128 bit [132] and can already reach a bit rate of 50 kbps [133]. Last, but not least, the promising printed electronics [134] has already become a hot research topic for companies [135], and its market, which was estimated by Idtechex in $1.92 billion in 2009, could rise up to $57.16 billion in 2019 [136].

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120. Paasch, G., Scheinert, S., Herasimovich, A., Hörselmann, I., Lindner, Th.: Phys. Stat. Sol. (a) 3, 534–548 (2008) 121. Ahles, M., Schmechel, R., von Seggern, H.: Appl. Phys. Lett. 85, 4489 (2004) 122. Erlen, C., Lugli, P., Fiebig, M., Schiefer, S., Nickel, B.: J. Comput. Electron. 5(4) (December 2006) 123. Berliocchi, M., Manenti, M., Bolognesi, A., Di Carlo, A., Lugli, P., Paolesse, R., Mandoy, F., Di Natale, C., Proietti, E., Petrocco, G., D’Amico, A.: Semicond. Sci. Technol. 19, 354, (2004). 124. Baude, P.F., Ender, D.A., Haase, M.A., Kelley, T.W., Muyres, D.V., Theiss, S.D.: Appl. Phys. Lett. 82, 3964 (2003). 125. Hoon Han, S., Cho, S.M., Kim, J.H., Won Choi, J., Jang, J., Hwan Oh, M.: Appl. Phys. Lett. 89(093504) (2006). 126. Kim, F.S., Guo, X., Watson, M.D., Jenekhe, S.A.: Adv. Mater. 21, 15 (2009) 127. Smith, J., Hamilton, R., Heeney, M., de Leeuw, D.M., Cantatore, E., Anthony, J.E., McCulloch, I., Bradley, D.D.C., Anthopoulos, T.D.: Appl. Phys. Lett. 93(253301) (2008) 128. IEEE Standard for Test Methods for the Characterization of Organic Transistors and Materials, IEEE Std 1620–2008. http://ieeexplore.ieee.org/servlet/opac? punumber=4695965 (2008) 129. IEEE Standard for Test Methods for the Characterization of Organic TransistorBased Ring Oscillators, IEEE Std 1620.1–2006. http://ieeexplore.ieee.org/servlet/ opac?punumber=4014407 (2006) 130. Mabeck, J., Malliaras, G.: Anal. Bioanal. Chem. 384(34353) (2006) 131. Roberts, M.E., Mannsfeld, S.C.B., Queralt o, N., Reese, C., Locklin, J., Knoll, W., Bao, Z.N.: Proc. Natl. Acad. Sci. USA 105(1213439) (2008) 132. Myny, K., Beenhakkers, M.J., van Aerle, N.A.J.M., Gelinck, G.H., Genoe, J., Dehaene, W., Heremans, P.: IEEE ISSCC Dig. Tech. Papers 52 (2009) 133. Elfrink, R., Pop, V., Hohlfeld, D., Kamel, T., Matova, S., de Nooijer, C., Jambunathan, M., Goedbloed, M., Caballero Guindo, L., Renaud, M., Penders, J. and van Schaijk, R.: First autonomous wireless sensor node powered by a vacuum-packaged piezoelectric MEMS energy harvester. In: IEEE International Electron Devices Meeting—IEDM, pp. 543–546. Baltimore, MD, USA, 7–9 Dec 2009 134. Gamota, D.R., Brazis, P., Kalyanasundaram, K., Zhang, J.: Printed Organic and Molecular Electronics, Kluwer Academic Publishers, New York (2004) 135. International Electronics Manufacturing Initiative (iNEMI) consortium. http://thor.inemi. org/webdownload/RI/2009_Research_Priorities.pdf (2009) 136. Das, R., Harrop, P.: Printed and Thin Film Transistors and Memory 2009–2029, Updated in Q3 2010. IDTechEx, United Kingdom. http://www.idtechex.com/research/reports/printed_ and_thin_film_transistors_and_memory_2009_2029_000221.asp?viewopt=showall (2010)

Chapter 2

Three-Dimensional Silicon–Germanium Nanostructures for CMOS-Compatible Light Emitters D.J. Lockwood and L. Tsybeskov

Abstract The present status of light emitters based on SiGe nanostructures is reviewed. To be commercially valuable, these light emitters should be efficient, fast, operational at room temperature, and, perhaps most importantly, compatible with the “main stream” CMOS technology. Another important requirement is in the emission wavelength, which should match the optical waveguide low-loss spectral region, i.e., 1.3–1.6 μm. Among other approaches, epitaxially grown Si/SiGe quantum wells and quantum dot/quantum well complexes produce efficient photoluminescence (PL) and electroluminescence (EL) in the required spectral range. Until recently, the major roadblocks for practical applications of these devices were strong thermal quenching of the luminescence quantum efficiency and a long carrier radiative lifetime. The latest progress in the understanding of physics of carrier recombination in Si/SiGe nanostructures is reviewed, and a new route toward CMOS-compatible light emitters for on-chip optical interconnects is proposed.

Introduction Optical interconnects in the form of fiber optics have been used for many years in different long-distance communication applications [1, 2]. With the microprocessor clock speed approaching 10 Gbps, optical interconnects are now being considered for on-chip interconnects as an alternative to metal wires with their unavoidable RC delay, significant signal degradation, high power dissipation, and electromagnetic interference [2–6]. Two major avenues toward optical interconnects on a chip include a hybrid approach with densely packaged III–V optoelectronic components [7–16] and the all-group-IV approach (mainly Si, Ge, and SiGe), where all the major components, e.g., light emitters, modulators, waveguides, and photodetectors, are monolithically integrated into the CMOS environment [17–20]. For almost five D.J. Lockwood (B) Institute for Microstructural Sciences, National Research Council Canada, Ottawa, Ontario K1A 0R6, Canada e-mail: [email protected]

A. Korkin et al. (eds.), Nanotechnology for Electronics, Photonics, and Renewable Energy, Nanostructure Science and Technology, DOI 10.1007/978-1-4419-7454-9_2,  C Springer Science+Business Media, LLC 2010

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decades, the efforts for obtaining light emission from group IV semiconductors have been mainly focused on porous silicon [21–24], silicon/silicon dioxide superlattices [25–29], silicon nanoprecipitates in silicon dioxide [24, 30], erbium in silicon [31], silicon/germanium quantum wells [32–34], and, more recently, iron disilicide [35]. However, no approach has so far been applied commercially. There are several reasons, including the lack of a genuine or perceived compatibility with conventional CMOS technology, the long carrier radiative lifetime in Si-based nanostructures (NSs), and, especially in the case of near-infrared emitters, the significant thermal quenching of the luminescence quantum efficiency [10].

Light Emission in Crystalline Silicon and Germanium Single-crystal Si (c-Si) and Ge are both indirect band gap semiconductors, and, in their pure state, direct electron–hole recombination without momentum conservation is forbidden (Fig. 2.1). To conserve momentum, an interaction with a phonon of appropriate wave vector is needed, and in low-temperature c-Si photoluminescence (PL) spectra one can see a complete set of characteristic Si phonons (Fig. 2.1). This type of electron–hole recombination is known as a phonon-assisted process [36– 40]. This phonon-assisted, slow (≥10−3 s) radiative recombination competes with a variety of much faster non-radiative carrier recombination mechanisms, including recombination via structural defects, impurities, surface states, and Auger recombination. Also, the low free exciton binding energy of ~15 meV is responsible for a fast decrease in the PL quantum efficiency as temperature increases. Despite this unfavorable situation, low-temperature luminescence in c-Si could be quite efficient, because there are several possibilities to effectively suppress non-radiative recombination. For example, epitaxially grown c-Si has an extraordinarily low concentration

E

Energy (E)

Si

(b)

(a)

(c)

Conduction band Radiative recombination

Photon (hv)

Phonons

hv NP

Momentum (k) Valence band

k

Fig. 2.1 Schematic of electron–hole recombination in (a) a direct band gap semiconductor and (b) an indirect band gap semiconductor with phonon assistance (the Si phonon spectrum is used as an example). (c) Low-temperature Si PL spectrum with the characteristic phonon sidebands indicated: NP—zero-phonon (also called the no-phonon (NP)) or direct exciton recombination, TA—transverse acoustic phonon, and TO—transverse optical phonon. The second replica of the TO phonon is separated from the main TO PL peak by ~60 meV

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of unwanted impurities and structural defects (~1012 cm−3 ). By decreasing the temperature and forming excitons, especially excitons bound to impurities, carrier diffusion is suppressed and the probability for a carrier to find a non-radiative recombination center is strongly reduced. Therefore, high-quality Si samples at low temperature might have a luminescence quantum efficiency close to 0.1% or even better [40–42]. A possibility to achieve a higher luminescence quantum efficiency is to passivate the c-Si surface with hydrogen, which leads to a strong reduction of the surface state density [43]. A similar effect can be obtained by electrochemical etching and formation of small-size Si crystallites with nearly perfectly hydrogenpassivated surfaces, as has been shown for anodically etched porous Si [21, 22]. It is also important to remember that the refractive index of c-Si is relatively high (≥3.5), and some appropriate sample preparation is necessary to extract light with low losses [44]. One of the possibilities is to use a photonic crystal fabricated using a submicron-thick Si-on-insulator (SOI) layer; it has been shown that the luminescence external quantum efficiency increases 70 times compared to that in bulk, ~100 μm thick surface polished c-Si samples [45]. Thus, despite the fact that the radiative lifetime in c-Si remains long, different sample preparation techniques could result in a dramatic difference in the PL external quantum efficiency. One quite different approach is to increase the internal luminescence quantum efficiency: mainly by relaxing the carrier recombination selection rules and accelerating the radiative recombination rate. In principle, this can be done by several methods: by changing the Si crystal structure (high pressure, strain, heavy doping, etc.) [40, 46]; by using radiative impurities such as rare earth, deep-level isoelectronic complexes (see Fig. 2.2 and [31, 46]); by forming extremely small Si

E (a)

(b) hv k

Fig. 2.2 (a) Schematic of carrier recombination in an indirect band gap semiconductor involving a deep energy level associated with an impurity. Note that for a localized carrier (e.g., an electron at an isoelectronic trap), the momentum is not well defined and it is stretched over the entire Brillouin zone; thus, electron–hole recombination no longer needs phonon assistance. (b) Low-temperature PL spectra in c-Si with nitrogen–carbon impurity complexes responsible for deep-energy levels and sharp PL features around 1.6 μm. (Reprinted with permission from [46], Copyright 1989, Elsevier)

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crystallites comprised of just a few atoms and exploiting the quantum confinement effect [47–49]. This work has received much attention; it is well covered in [17, 18] and will not be discussed here. An alternative approach is to create carrier recombination conditions involving strong electron–electron interactions. Compared to the other approaches, the latter one has received relatively little attention, and it will be briefly presented next. The most well-known feature of strong carrier–carrier interactions in group IV semiconductors is the electron–hole condensation and the formation of electron– hole droplets (EHDs) [50]. This process is mainly possible due to a long carrier radiative lifetime in pure Si and Ge crystals, but it also requires a combination of low temperature and high carrier concentration. At low temperature, electrons and holes quickly form free excitons (FE). The process of EHD condensation from the electron–hole FE gas into the electron–hole liquid (EHL) is a type I phase transition [50–53] (Fig. 2.3). In practice, a high level of excitation often produces an electron– hole plasma (EHP), a thermodynamic phase where the carrier–carrier interaction becomes comparable with the electron–lattice interaction. Thus, the condensation of the EHL and formation of EHDs could be achieved from both thermodynamic states (Fig. 2.3). The EHD luminescence is quite efficient, despite the fact that it remains a phonon-assisted process with typical phonon features in the PL spectra (Fig. 2.3). The phonon features are shifted to lower photon energies (due to additional carrier–carrier interactions), strongly broadened, and the measured PL transient characteristics indicate a carrier lifetime as short as ~10−8 s [54–56]. The details of the recombination mechanisms will not be discussed here, but a qualitative model suggests that the carrier–carrier interaction within EHDs is responsible for partial “whitening” of the phonon spectra (i.e., c-Si lattice field screening), and it produces a relaxation of selection rules and a shortening of the carrier radiative lifetime [56]. One of the limiting factors of the EHD condensation is exciton diffusion, and it has been shown that in ultra-thin (<100 nm) layers of SOI, EHD

Temperature, K

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FE gas EH Plasma

EHD or e-h plasma

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(c)

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30 20 10 16 10

FE TO

EHD TO

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hv EHD TA

EH liquid

k 1017

1018

1019

1

1.04

1.08

1.12

1.16

Photon energy (eV)

Carrier density, cm–3

Fig. 2.3 (a) Phase diagram showing transitions from electron–hole (EH) free exciton (FE) gas to EH liquid and EH plasma in c-Si. (b) Phonon-assisted electron–hole recombination is shown with partial whitening of the phonon dispersion. (c) The PL spectrum in c-Si at 10 K and carrier density ≥1016 cm3 showing coexisting FE and electron–hole droplet (EHD) PL peaks

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condensation occurs at a lower carrier concentration compared to that in bulk c-Si [57]. Also, it has been shown that at a temperature higher than the thermodynamic limit for electron–hole condensation, an EHP can be produced instead of EHDs [50, 53]. EHP radiative recombination in c-Si is also much faster (τEHP ≈ 10−7 s) compared to low-excitation electron–hole recombination (τe−h ∼ 10−3 s), but at this level of excitation it competes with Auger recombination. Auger recombination has a lifetime τAuger = 1/Cn2 , where n is the carrier concentration, and for bulk silicon C ≈ 10−30(−31) for electrons (holes), respectively [58]. Thus, at a carrier concentration approaching the EHP regime (~1018 –1019 cm−3 ), Auger recombination quickly becomes the dominant recombination channel. The majority of text books consider Auger recombination as a strictly nonradiative process where the recombining electron and hole pair (e–h) transfers its energy and momentum to a third particle, which could be either an electron (e) or a hole (h). Thus, Auger processes could be divided into two major categories: (i) two electrons–one hole (e–h, e) with generation of a “hot” electron in the conduction energy band and (ii) two holes–one electron (e–h, h) with generation of a “hot” hole in the valence energy band. Depending on the energy band structure, these hot carriers can dissipate their energy by generating multiple phonons (i.e. heat generation), or they could be transferred into another energy band inside the Brillouin zone. In c-Si, the bottom of the conduction energy band is in the X-valley. The second lowest conduction energy band is on the other side of the Brillouin zone in the L-valley, and it is separated from the bottom of the conduction energy band by an energy of 0.89 eV, which is comparable with the energy gap EG = 1.1 eV at room temperature

E

E (a)

(b)

Si

Ge

X

L

X

L

e-h, e e-h, e <100> E G

Γ

HH

<111> k

LH

SO

Γ

<100>

EG

HH

<111> k

LH

e-h, h SO

Fig. 2.4 Schematic of the energy band structure for –X (in <111> direction) and –L (in <100> direction) vicinities in (a) c-Si and (b) c-Ge with possible Auger-mediated electron (e) and hole (h) inter-valley transitions. Heavy-hole (HH), light-hole (LH), and split-off (SO) valence bands are shown and the fundamental energy gap is denoted by EG

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(Fig. 2.4a). At the -point (i.e., the center of the Brillouin zone), the c-Si conduction band minimum is 4.2 eV higher than the maximum of the valence energy band. This conduction energy band structure makes electron transfer between different valleys very unlikely. However, hot electrons in c-Si produced by high electric field in a reverse bias p–n junction or a metal-oxide-semiconductor (MOS) device have a wide range of energies and momenta; they might recombine with holes and produce “white” light with photon energies ranging over 1.1 eV ≤ hv < 4.2 eV but with a low quantum efficiency [42, 59]. Single-crystal Ge (c-Ge) is also an indirect band gap semiconductor, but with a very different energy band structure (Fig. 2.4b). The indirect energy gap is EG = 0.66 eV (at temperature T = 300 K) with the conduction energy band minimum  = 0.8 eV with an in the L-valley, but the direct energy gap at the -point is EG energy separation between the two neighboring conduction bands of only 0.14 eV (Fig. 2.4b). Thus, the probability of electron transfer from indirect (L) to direct () band is much higher compared to that in c-Si. Another important feature of the c-Ge energy band structure is the energy separation of 0.29 eV between the point and split-off (SO) band (Fig. 2.4b). Therefore, a variety of the carrier transfer processes between different energy valleys in both (conduction and valence) energy bands are possible [60, 61]. One of them is the electric field induced electron transfer from indirect to direct energy band—the L– process, which was first discovered by Gunn in n-type Ge [62]. In p-type Ge, the Auger process could mediate hole transfer from the -point to the bottom of the SO band [63] (Fig. 2.4b). Carrier transfer in cGe followed by radiative electron–hole recombination produces light emission in the desired spectral region of 1.2–1.6 μm (Fig. 2.5). Unfortunately, the c-Ge conduction energy band near the -point has a density of states approximately 10 times lower compared to that in the L-valley, and fast electron back transfer suppresses the direct band electron–hole radiative recombination [64, 65]. Several possibilities to reduce the back transfer, including the use of degenerate n-type c-Ge and strain have been discussed, but none of them has so far produced efficient light emission associated with c-Ge direct band gap radiative electron–hole recombination.

Light Emission in SiGe Bulk Alloys and Composition-Controlled Quantum Wells Since both c-Si and c-Ge are indirect band gap semiconductors, it is a common assumption that SiGe crystalline alloys should also exhibit properties of an indirect band gap semiconductor. Actually, the entire concept of k-space is applicable to a crystal lattice with an atomically perfect long range order. SiGe alloys are crystalline material but with strong compositional disorder (i.e., the absence of long range order in the position of Si and Ge atoms within a SiGe crystal lattice). As a result of this compositional disorder, carrier recombination selection rules in SiGe alloys are partially relaxed. This conclusion is supported by Fig. 2.6, where instead of a totally suppressed zero-phonon transition, which is normally observed in lowtemperature PL spectra of high-quality single-crystal Si and Ge, SiGe bulk alloys

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Fig. 2.5 Low-temperature PL spectra in p-type Ge in the vicinity of fundamental, indirect energy gap (IG), direct gap (DG), and above-the-gap electronic transitions. (Reprinted with permission from [63], Copyright 1984, American Physical Society)

exhibit PL spectra showing both phonon-assisted and zero-phonon radiative transitions in the spectral region of 1.3–1.6 μm (see [66]). The relaxation of carrier recombination selection rules in SiGe alloys produces PL that is faster compared to that in Si but still orders of magnitude slower compared to the recombination time in direct band gap semiconductors. As the temperature increases, the PL intensity quickly decreases with a thermal quenching activation energy of ~10–15 meV, which has been attributed to the binding energy of an exciton localized on SiGe stoichiometry fluctuations [66–68]. Therefore, this type of luminescence in SiGe bulk crystalline alloys has little practical importance. Epitaxial growth of pure Ge on Si is complicated by the 4.2% lattice mismatch (see, for example, a review article [69]). To avoid formation of structural defects (mainly dislocations) with a large number of non-radiative recombination centers, controlled-composition Si1−x Gex alloys with 0.1 < x < 0.2 can be grown by using techniques such as molecular beam epitaxy (MBE) or ultra-high vacuum (UHV) chemical vapor deposition (CVD). These heterostructures exhibit a low defect density at interfaces, and Si/Si1−x Gex multilayers with 0.1 < x < 0.2 were intensively studied as a possible method to confine electron–hole pairs in double heterojunction or quantum well (QW) configurations and to reduce the luminescence thermal

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Fig. 2.6 Low-temperature PL spectra in bulk Si1−x Gex alloys for a wide range of compositions x. (Reprinted with permission from [66], Copyright 1989, American Physical Society)

quenching. An intense luminescence, but still restricted to low temperature, has been demonstrated in Si/Si1−x Gex quantum wells and superlattices with x ≤ 0.2 (see Fig. 2.7 and also [70]). Several studies have been specifically focused on the determination of the energy band alignment (i.e., type I or type II, see Fig. 2.8) in these nanostructures (NSs), but so far no final conclusion has been reached [71–73]. It has also been shown that SiGe interdiffusion during growth of Si/Si1−x Gex QWs can be minimized using a relatively low growth temperature (<550◦ C). On the other hand, SiGe epitaxial growth at temperatures below 500◦ C usually produces a significant density of dislocations [73–75]. Thus, high-quality Si/Si1−x Gex QWs with x < 0.2 can be grown using only a relatively narrow processing growth “window,” but again the PL quantum efficiency thermal quenching remains the unresolved problem for practical light emitters at 1.3–1.5 μm.

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Fig. 2.7 Low-temperature PL spectra in Si/Si1−x Gex /Si single quantum wells (see inset) with composition 0.1 < x < 0.25. (Reprinted with permission from [70], Copyright 1992, American Institute of Physics)

TYPE II EC (a) Si EV

Fig. 2.8 Schematic representation of (a) type I and (b) type II energy band alignments supposed to exist in Si/SiGe NSs. EC and EV are the energies of the conduction and valence bands, respectively, in Si and Si1−x Gex

Si Si1-xGex TYPE I

EC Si EV

Si Si1-xGex

(b)

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Properties of SiGe Three-Dimensional Nanostructures By the 1990s, a different form of SiGe NS, namely the three-dimensional (3D) selfassembled system produced by the well-known Stranski-Krastanov, or cluster layer, growth mode in lattice-mismatched materials, had been demonstrated [76–80]. It has been shown that dislocation-free SiGe growth can be achieved using a higher temperature (≥600◦ C), and that the non-planar geometry is mainly responsible for the significant increase of the SiGe critical layer thickness. It has also been found that, compared to two-dimensional (2D) Si/SiGe NSs, the PL and electroluminescence (EL) quantum efficiency in 3D Si/SiGe NSs is higher (up to 1%), especially for T > 50 K [81–84]. Despite many successful demonstrations of PL and EL in the spectral range of 1.3–1.6 μm, which is important for optical fiber communications, the proposed further development of 3D Si/SiGe-based light emitters was discouraged by several studies indicating a type II energy band alignment at Si/SiGe heterointerfaces [72, 85–87], where the spatial separation of electrons (located in Si) and holes (localized in SiGe) (see Fig. 2.8) was thought to make carrier radiative recombination very inefficient. Later, it was also shown that 3D Si/SiGe NSs exhibit an extremely long (of the order of 10−2 s) luminescence lifetime [88], which is of the order of a million times longer than in III–V semiconductors and their NSs. Thus, according to this analysis, 3D Si/SiGe NSs cannot be used to achieve efficient and commercially valuable light-emitting devices. Recently, however, it has been shown that despite the fact that the Si/SiGe heterointerface most likely exhibits type II energy band alignment, it is still possible to obtain conditions favorable for an efficient carrier radiative recombination. The rest of this review presents the revised understanding of basic physics in such systems and demonstrates that the radiative carrier recombination lifetime can successfully be reduced from 10−2 s to 10−7 s, which is only ~10 times longer than that found in direct band gap III–V semiconductors.

Growth and Structural Properties of Si/SiGe Three-Dimensional Nanostructures The standard fabrication of Si/SiGe NSs is in the form of a Si/SiGe multilayer structure, which could be a planar layer–layer or 2D structure, or a layer–cluster system which by the definition is a 3D NS. Both types of fabrications are based on the sequential physical sputtering of Si and Ge (SiGe) in MBE or thermal decomposition of SiH4 and GeH4 in CVD, and it takes place at a temperature in the range T = 500 − 650◦ C. At those temperatures, both the high Ge solid solubility in Si and strain-induced SiGe interdiffusion due to the ~4% lattice mismatch between Si and Ge are important. The MBE growth provides a better control over the average SiGe cluster composition, although, because of interdiffusion during growth, the composition is not uniform within the cluster volume [89–92]. Figure 2.9 shows cross-sectional transmission electron micrographs (TEM) and top view scanning electron micrographs of Si/SiGe NSs formed by MBE at different temperatures and

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SiGe

SiGe

Si substrate (a)

(b)

500 nm

(c)

500 nm

(d)

Fig. 2.9 (a) Cross-sectional TEM showing MBE grown Si/SiGe multilayer 2D NSs with a Ge composition close to 30% and grown at T = 550◦ C and (b) a cross-sectional TEM micrograph focusing on a single SiGe layer showing its epitaxial nature and some “waviness” of the upper SiGe/Si interface. A larger scale SEM top view of a Si/SiGe single layer with a Ge composition close to 50% and grown at temperatures of (c) 570◦ C and (d) 600◦ C showing a clearly observable increase in density of SiGe clusters at higher temperature

depicts the transition from 2D (layer) to 3D (a cluster) growth modes. In general, SiGe cluster growth at temperatures TG ≥ 550◦ C commences with the spontaneous development of a Si1−x Gex planar, <1 nm thick, wetting layer where x varies, mainly due to uncontrolled SiGe interdiffusion. With the further influx of Ge and Si, the growth mode then switches from 2D to 3D, and this helps release some of the lattice mismatch-induced strain [92, 93]. The fully grown, 3–10 nm high, and initially nearly pyramidal-shaped SiGe clusters (Fig. 2.10a) have a Ge-rich (~50% depending on the Ge flux) core, although the exact final cluster shape and composition strongly depend on the fabrication conditions, mainly deposition temperature and time [89– 91]. If the SiGe cluster is covered by a Si cap, the initial pyramid-like cluster top is smoothed out, and the capping Si layer is locally strained, mostly near the top of the SiGe cluster. In multilayer Si/SiGe cluster samples with a thin (<10 nm) Si layer between SiGe cluster layers, this strain field propagates in the growth direction, and it induces vertical SiGe cluster self-ordering (Fig. 2.10b). In these Si1−x Gex clusters, the chemical composition x has been recently studied using the technique of analytical TEM (see Fig. 2.11 and also [89]). Detailed structural analysis also

52

D.J. Lockwood and L. Tsybeskov

Fig. 2.10 (a) Cross-sectional TEM of a pyramidal-shaped SiGe cluster grown by MBE on Si without a Si capping layer. (b) Cross-sectional TEM of a multilayer 3D Si/SiGe NS clearly showing cluster vertical self-alignment. The growth was performed at 650◦ C

Z Si

20 nm

(a)

Composition (%)

100 80

(b)

Si

60 40 20 0 –10

Ge 0

10 Z (nm)

20

30

Fig. 2.11 (a) TEM micrograph showing the vertical direction of the compositional analysis of a SiGe cluster and (b) the distribution of Si/Ge atomic composition in that cluster. The Z direction is the direction of growth and Z = 0 corresponds to c-Si substrate surface

2

Three-Dimensional Silicon-Germanium Nanostructures

53

indicates that Si in the valleys between SiGe clusters is slightly compressed [49]. An increase in SiGe cluster height results in an increase of their lateral size and change of the cluster shape known as the pyramid–dome transition [79, 80, 89, 94]. These SiGe dome-shaped clusters have multiple facets (Fig. 2.11) and, therefore, might have some structural defects at SiGe/Si interfaces. To summarize, buried SiGe clusters with the highest Ge composition of near 50% in the middle of the clusters and typical cluster height of <10 nm are surrounded by Si, which is tensile strained above each cluster and compressed laterally between clusters to maintain a low overall strain. Each SiGe cluster consists of Si1−x Gex crystalline alloys with x increasing toward the cluster center. Thus, despite being fully crystalline materials, 3D Si/SiGe NSs with a high (~50%) Ge atomic concentration exhibit significant embedded strain and compositional disorder. Further insight into the structural properties of the various SiGe multilayers grown by MBE discussed here is revealed by X-ray and Raman scattering experiments. Figure 2.12 compares the (004) rocking curves from three Si1−x Gex /Si multilayers with 0.09 < x < 0.55. The diffraction data from the sample with the lower Ge composition is very well reproduced by the calculation using the structural parameters of Table 2.1. The agreement for the sample of intermediate composition is also good, but a damping of the higher order satellites (near 2θ = 66◦ ) indicates a loss of coherence of the superperiodicity due to either thickness irregularities or loss of interface sharpness. No good simulation of the data could be obtained for samples with high Ge composition (x > 0.5). Here the satellites remain relatively sharp, but they are broadened at the base and the usual thickness fringes between the peaks are not observed. The result shown here is typical of superlattices exhibiting undulated interface morphology such as that depicted in Fig. 2.10b [80]. Although the sample shown here has a nominal Ge composition of 0.53, a better fit was obtained using a lower Ge composition; here, in Fig. 2.12c, a value of x = 0.42 was used. Although the conventional diffraction theory of layered media cannot accurately model structures with non-planar interfaces, the lower Ge composition found here points to Si–Ge atomic exchange during the island formation. This aspect has been discussed in detail elsewhere [90, 91]. Figure 2.13 presents the specular reflectivity curves measured on the same samples as in Fig 2.12. As for the rocking curves, reflectivity curves exhibit satellites arising from the periodic nature of the multilayers. Here, however, the contrast is primarily caused by the modulation of the atomic number in the growth direction rather than by the strain, and analysis of the reflectivity provides complementary information on the surface and interface roughness. Also shown in Fig. 2.13 are simulated profiles obtained with the same values for the thicknesses and compositions used in the rocking curve simulations of Fig. 2.12 (see Table 2.1). Here, the interface abruptness is an additional fitting parameter that is taken into account in the calculations by introducing a phenomenological Debye–Waller interface roughness parameter σ at each individual interface. Simulations obtained by assigning constant values for the interface roughnesses σ Si and σ Ge to all Si to Si1−x Gex and Si1−x Gex to Si interfaces, respectively, are in qualitative agreement with the experiment. In all cases, a departure between experiment and calculation is seen at higher

54

D.J. Lockwood and L. Tsybeskov 106

(a)

105 104 103 102 101 100 66

Intensity (cps)

106

67

68

69

70

67

68

69

70

68

69

70

(b)

105 104 103 102 101 100 66

106

(c)

105 104 103 102 101 100 66

67

2θ (degree)

Fig. 2.12 Experimental (black) and simulated (red) (004) rocking curves from the Si1−x Gex /Si multilayers with (a) x = 0.09, (b) x = 0.17, and (c)x = 0.53. Note that in the latter case, the calculation shown here corresponds to x = 0.42

angles of incidence and is the result of superlattice irregularities and/or interface blurring. Based on the simulations, the value of σ Ge is systematically larger than that of σ Si and the difference increases for higher Ge concentrations, consistent with the evolution of the alloy layers to a 3D morphology in Ge-rich structures. Additional information on the spatial coherence of the interfaces in multilayers can be obtained by recording the X-ray scattered intensity about a strong diffraction peak in a reciprocal space map (RSM). Figure 2.14 compares the (004) RSM from

2

Three-Dimensional Silicon-Germanium Nanostructures

55

10–1

(a)

10–2 10–3 10–4 10–5 10–6 10–7

0

1

2

3

4

Intensity (arb. units)

10–1

(b)

10–2 10–3 10–4 10–5 10–6 10–7 0

1

2

3

4

5

10–1

(c)

10–2 10–3 10–4 10–5 10–6 10–7

0

1

2

3

4

5

6

2θ (degree) Fig. 2.13 Experimental (black) and simulated (red) (004) rocking curves from the Si1−x Gex /Si multilayers with (a) x = 0.09, (b) x = 0.17, and (c) x = 0.53. The simulated reflectivity curves were calculated using the structural parameters determined from the high-resolution X-ray rocking curve analysis. Distinct roughness parameters σ Si and σ Ge , as given in Table 2.1, were assigned to the Si to Si1−x Gex and Si1−x Gex to Si interfaces. These were assumed to be constant throughout the structures. The simulation also included a surface oxide layer of 0.6 nm roughness and 2 nm thickness for x = 0.09 and 0.17 and 1 nm thickness forx = 0.53

the various samples. In these maps, the horizontal direction h corresponds to the Xray wave vector component in a direction parallel to the surface, while the vertical direction l is the wave vector component in the growth direction. While the rocking curves of Fig. 2.12 correspond to the integrated intensity in a vertical direction, the

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D.J. Lockwood and L. Tsybeskov

Table 2.1 Growth and physical data on the Si1−x Gex /Si multilayer samples grown by MBE, where x is the nominal Ge composition, tSi is the nominal thickness of the Si spacer layers, tSiGe is the nominal thickness of the Si1−x Gex layers, N is the number of periods, Tgrowth is the growth temperature, RSi is the Si deposition rate, RGe is the Ge deposition rate, and σ Si and σ Ge are the Si to Si1−x Gex and Si1−x Gex to Si interface roughness, respectively, as determined from X-ray reflectance studies x

tSi (nm)

tSiGe (nm)

N

Tgrowth (◦ C) RSi (nm/s) RGe (nm/s) σ Si (nm) σ Ge (nm)

0.091 0.17 0.53 0.56 0.61

27 34 15 13.6 14.1

3.8 7.0 3.5 3.0 3.0

20 15 10 10 10

595 595 625 640 650

(a)

(b)

0.2 0.2 0.075 0.07 0.07

0.05 0.05 0.09 0.09 0.09

(c)

0.5 0.5 0.6 0.7 –

0.7 0.9 0.9 1.0 –

(d)

105

Log Intensity (cps)

104

103

102

101

100

h

h

h

h

Fig. 2.14 Reciprocal space maps about (h, k, ) = (0, 0, 4) for four Si1−x Gex /Si multilayers with (a) x = 0.09, (b) x = 0.17, (c) x = 0.53, and (d) x ≈ 0.6. Here the intensity is shown on a logarithmic scale. The horizontal and vertical scale markers correspond to h = 0.001 and  = 0.005, respectively

RSM provides details on the actual shape of the various satellite features and reveals additional X-ray scattering away from Bragg conditions. In the RSM, the superperiodicity is revealed by the presence of equally spaced satellite spots aligned in a vertical direction. Interesting differences between samples can be noted by comparing the various RSMs of Fig. 2.14. First, the sample with x = 0.091 presents satellites that have the smallest full width h = 0.0008 in the h direction. Samples with x = 0.17 and 0.53 exhibit broader satellites with h = 0.001. More interestingly, the latter sample displays side lobes arising from a periodic modulation of the

2

Three-Dimensional Silicon-Germanium Nanostructures

57

Si-Si

Normalized Raman signal (arb. units)

Si-Ge Ge-Ge

x = 0.53

x = 0.17

x = 0.09

100

200

300

400

500

600

Raman shift (cm–1) Fig. 2.15 Evolution of Raman spectra in 3D Si1−x Gex /Si samples with x increasing from 9 to 53%

interfaces similar to that depicted in Fig. 2.10a and this is discussed in detail elsewhere [90, 91]. The sample with x = 0.61 exhibits broader diffuse satellites with h = 0.002. This RSM is typical of Ge-rich (x > 0.6) multilayers and indicates a significant loss of interfacial perfection and shorter coherence length both parallel and perpendicular to the interface. Figure 2.15 compares Raman spectra in samples with Si1−x Gex /Si 3D nanostructures with 0.09 < x < 0.55. In Si1−x Gex islands with a low Ge content (x = 0.091) we observe a Raman signal attributed to Si–Si vibrations with a main, zone-center optical phonon peak at ~520 cm−1 and a weaker signal at ~300 cm−1 associated with Si acoustic phonons (see, for example, [80]). No significant Raman peaks associated with Ge–Ge vibrations at 290 cm−1 , Si–Ge vibrations at ~420 cm−1 [80], and an amorphous Si phase at ~ 480 cm−1 were found. An increase in Ge content up to x = 0.17 increases the intensity of the Raman peak associated with Si–Ge vibrations at ~420 cm−1 . However, the Raman signal associated with Ge–Ge vibrations at ~310 cm−1 is still quite weak. Further increase in the Ge content (x = 0.53) in 3D Si1−x Gex nanostructures produces strong Raman signals at ~310 cm−1 related to Ge–Ge vibrations and at 420 cm−1 related to Si–Ge vibrations. Note that in the

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D.J. Lockwood and L. Tsybeskov

sample with x = 0.53, the Si–Si vibration-related peak at ~520 cm−1 broadens significantly, due to an increase in built-in strain, which in Si1−x Gex /Si samples with thicker Ge layers can be entirely localized within the Si spacer layers [93]. Another important observation is the absence of a-Si and a-Ge phases, showing that the islands in Si1−x Gex /Si multilayers are true crystalline alloys.

Light-Emitting Properties of Si/SiGe Three-Dimensional Nanostructures In a system with strong selection rule relaxation (e.g., semiconductor bulk alloys), carrier recombination provides a higher PL quantum efficiency compared to that in an indirect band gap semiconductor, e.g., single-crystal Si and Ge. PL measurements in Si/SiGe NSs reveal a significantly enhanced intensity ratio between no-phonon (NP) luminescence and phonon-assisted luminescence compared to c-Si (Fig. 2.16). Thus, systematic studies of the PL spectra in 3D Si/Si1−x Gex NSs with control over the average Ge atomic concentration x provide very important information regarding changes in the carrier recombination mechanism (e.g., selection rule relaxation and conduction and valence band alignment) as x increases from 0 (c-Si) to ~55%, which is the highest Ge composition in structural defect-free SiGe clusters. Fig. 2.16 Figure 2.17a compares PL spectra in MBE samples with x = 0.096, 0.16, and 0.53. For samples with x = 0.096, we find relatively narrow PL bands at 1.05 and

NP

SiGe WL

c-Si

PL Intensity (arb. un.)

PL Intensity (arb. un.)

TO TO

TA

NP TO + OG

0.90

0.93 0.95 Photon Energy (eV) (a)

0.98

1.05

TA

1.10 1.15 Photon Energy (eV) (b)

Fig. 2.16 Comparison between low-temperature (T = 4 K) PL spectra in (a) a SiGe wetting layer with a Ge concentration of ~20% and (b) undoped crystalline Si (c-Si). Note the dramatically different intensity ratios between the NP and TO phonon PL lines of the two samples.

2

Three-Dimensional Silicon-Germanium Nanostructures

(a)

59

3D Si1-xGex

(b)

(c) TO+OΓ

Fig. 2.17 Low-temperature (T = 4 K) PL spectra of MBE-grown Si/Si1−x Gex 3D NSs with the indicated average Ge atomic concentration x. The characteristic phonon-assisted transitions and the PL spectral shift due to an increase in Ge concentration are indicated by the labels and dashed line, respectively

1.11 eV (Fig. 2.17a) attributed to NP and TO phonon PL bands in Si-rich SiGe alloys [56–58]. Note that these PL bands are in the vicinity of c-Si luminescence, and that the intensities of these two sets of PL bands are comparable. Therefore, we conclude that a small amount of Ge (<10%) slightly reduces the SiGe band gap and mainly relaxes selection rules, increasing the ratio of NP/TO PL band intensities. The observed broadening of these two PL bands, compared to c-Si-related PL, is apparently due to the composition disorder resulting from the introduction of substitutional Ge atoms (~10%) into the c-Si matrix. Increasing the average Ge composition within Si1−x Gex clusters up to x = 0.16 results in significant changes in the PL spectrum (Fig. 2.17b). An intense PL band peaked at 0.95 eV has appeared, showing an effective SiGe band gap reduction of ~150 meV compared to c-Si. This broad and featureless PL band with a full width at half maximum (FWHM) of ~70 meV indicates a much stronger compositional disorder compared to 3D Si/SiGe NC samples with x = 0.096. The PL spectrum in the samples with an average Ge composition close to 53% (Fig. 2.17c) depicts a broad feature with a major PL peak centered at a photon energy of 0.75 eV; this peak energy is close to the band gap of crystalline Ge (c-Ge) at 4 K. A second PL peak is found at ~0.85 eV. These samples

60

T = 4K

NP PL Intensity (arb. un.)

Fig. 2.18 Low-temperature (T = 4 K) PL spectra in Si/SiGe 3D NSs grown by CVD. The PL spectrum is fitted quite well with two Gaussian peaks. The PL peak separation energy is close to the SiGe characteristic phonon energy of ~48 meV

D.J. Lockwood and L. Tsybeskov

TO

0.6

0.7

0.8 Photon Energy (eV)

0.9

have higher PL quantum efficiency than samples with lower x values. Both PL bands are quite broad, most likely due to compositional disorder, which is in agreement with the Raman scattering measurements. In contrast to MBE-grown samples, CVD growth of 3D Si/SiGe NSs does not provide precise control over the atomic composition, and, most likely, it produces more Si/SiGe interdiffusion at heterointerfaces [80]. This is well reflected in PL spectra, where no fine structure has been found (see Fig. 2.18). However, the broad and asymmetric PL peak is well fitted by two Gaussian bands, often identified as the NP and TO phonon lines [84] and separated by an energy of ~48 meV, which is close to the energy of characteristic SiGe phonons. Thus, there is at least a qualitative similarity between PL spectra in MBE- and CVD-grown 3D Si/SiGe NSs. Also, the PL efficiencies in MBE- and CVD-grown samples are comparable. Figure 2.19 summarizes the PL intensity as a function of excitation intensity in MBE samples having different average Ge atomic concentrations. The same linear dependence (on a log–log plot) for PL associated with c-Si and a sublinear (close to square root) dependence for PL associated with Ge-rich SiGe clusters has been found in nearly all 3D Si/SiGe NSs grown by both CVD and MBE. Studies of the PL spectra and intensity temperature dependence show that at low temperatures the PL intensity is nearly temperature independent (Figs. 2.20 and 2.21). At higher temperatures the PL intensity drops exponentially, and the activation energies of PL thermal quenching are shown in Fig. 2.21. There is a clear correlation between the Ge composition in Si1−x Gex 3D NSs and the PL intensity temperature dependence. For samples with a low (x = 0.096) Ge composition the activation energy Ea is ~10 meV, which is similar to that of the TO phonon peak

Three-Dimensional Silicon-Germanium Nanostructures

Fig. 2.19 The PL intensity as a function of excitation intensity in MBE-grown Si/Si1−x Gex 3D NS samples with the indicated average Ge concentration x. The PL bands associated with the cluster core, wetting layer (WL), and characteristic TO phonons are indicated

61

Si, TO x = 0.096

SiGe

3D Si1-x Gex

(a) PL Intensity (arb. units)

2

x = 0.16

Si, TO

3D Si1-x Gex (b)

SiGe

SiGe, cluster x = 0.53 SiGe, WL (c) 1

10 100 Excitation Intensity (W/cm2)

105 T = 4K

PL Intensity (arb. un.)

103 T = 75K T = 145K 101 T = 220K 10–1 Fig. 2.20 PL spectra in CVD-grown Si/SiGe 3D NSs measured with an excitation intensity of 5 W/cm2 at the indicated temperatures (the PL spectra have been shifted vertically for clarity)

T = 250K

10–3 0.8

0.9 1 Photon Energy (eV)

1.1

62 Ea~8 meV

x = 0.096 Ea~10 meV PL intensity (arb. un.)

Fig. 2.21 The PL intensity temperature dependence in MBE-grown Si/Si1−x Gex 3D NS samples with the indicated average Ge concentration x measured for different PL bands

D.J. Lockwood and L. Tsybeskov

TO-Si SiGe

x = 0.16

3D Si1-xGex

SiGe Ea~25 meV

x = 0.53

Ea~20 meV

SiGe, core Ea~60 meV 0

50

100 150 1000/T (K–1)

200

250

in c-Si (~8 meV), and the PL has almost vanished by 40 K. This result could be explained by the thermal dissociation of a nearly free exciton [84]. In samples with a higher (x = 0.16) Ge composition, the activation energy of PL thermal quenching is increased, and the PL is observable up to ~100 K (Fig. 2.21b). The broad PL band observed at 0.95 eV for the Si/Si1−x Gex sample of x = 0.16 exhibits an activation energy of ~25 meV, which combined with a sublinear dependence in PL intensity as a function of excitation intensity (Fig. 2.19b) is in contrast with the x = 0.096 sample. This observation suggests that the non-equilibrium carriers are spatially localized and that Auger recombination contributes to the overall recombination mechanism even at very low (~100 mW/cm2 ) excitation intensity. Most likely, in 3D Si/Si1−x Gex NSs with x = 0.16, the carriers (possibly holes) are localized within 3D quasi-wells. In 3D Si/Si1−x Gex NSs with x = 0.53 the PL spectrum contains two bands peaked at 0.85 eV and 0.75 eV (Fig. 2.17c). There are no characteristic phonons in the Si/SiGe system with an energy of ~100 meV, and it is thus reasonable to assume that the observed PL bands are associated with carrier recombination within two different regions of the 3D SiGe NSs. The PL band peaked at 0.85 eV has almost the same PL quenching activation energy (~20 meV) as in the sample with x = 0.16 while the PL intensity as function of excitation intensity is linear over a wide range of excitation intensities. The second PL band peaked at 0.75 eV has an activation energy of ~60 meV (Fig. 2.21c) and is nearly temperature independent up to 100 K. Because of its high quantum efficiency, it can be monitored almost up to room temperature. This data suggests that 3D Si/Si1−x Gex NSs with x = 0.53 contain coupled subsystems with different (lower and higher) Ge concentrations. It is quite

2

Three-Dimensional Silicon-Germanium Nanostructures

63

possible that a spatial localization of electron–hole pairs within 3D regions of higher Ge concentration, and thus having a lower band gap, could be responsible for the observed sublinear excitation dependence of the PL band at 0.75 eV (Fig. 2.19c). The remaining 3D regions with a lower Ge concentration (e.g., having a higher band gap) have a lower carrier concentration and the PL band (peaked at 0.85 eV) exhibits a linear excitation dependence. The PL thermal quenching observed in 3D Si/Si1−x Gex samples grown by MBE could be associated with different mechanisms. As mentioned earlier, the activation energies of the PL thermal quenching in samples with x = 0.096 and x = 0.16 are close to the observed exciton binding energy in SiGe alloys and Si/Si1−x Gex NSs. In samples with x = 0.53, the greater activation energy could be attributed to carrier diffusion from a 3D potential well. This assumption is justified by the expected type II band alignment in SiGe NSs with a deep (>100 meV) potential well for holes and a relatively small potential barrier for electrons [88]. Thus, phonon-assisted carrier tunneling can produce the observed ~60 meV activation energy for thermal quenching of the PL intensity. A continuous shift of the PL band from ~1 to 0.75 eV has been found previously in SiGe alloys with increasing Ge concentration [95–100]. Instead, in these 3D Si/Si1−x Gex samples with a Ge concentration higher than 50%, a simultaneous threshold-like appearance of two clearly resolved PL peaks at 0.85 and 0.75 eV is observed. This suggests that Ge segregation might take place as x increases up to ~0.5. Since the PL peak at 0.75 eV is close to the value of the band gap in pure cGe, we propose that such a segregation results in a Ge-rich core within a SiGe shell forming the 3D Si/Si1−x Gex NSs embedded within a pure Si matrix. It has been known for some time that the PL spectra in 3D Si/SiGe NSs, which are similar to that in III–V quantum wells with type II energy band alignment [101], exhibit a blue shift as the excitation intensity increases [63–64]. In our studies, this effect is found in both MBE- and CVD-grown samples. Figure 2.22 shows PL

PL Intensity (arb. units)

Fig. 2.22 PL spectra in CVD-grown Si/SiGe Si/SiGe 3D multilayer samples measured at T = 8 K under different (indicated) excitation intensities

T = 8K

TO

SiGe Cluster 2

100 mW/cm

c-Si

2

1 W/cm

2

5 W/cm

2

10 W/cm

TO+OΓ

TA

SiGe WL

0.8

0.9

1.0

PL Photon Energy (eV)

1.1

64

D.J. Lockwood and L. Tsybeskov

spectra in a CVD-grown sample measured under excitation intensities varying from 0.1 to 10 W cm−2 . At the lowest excitation intensity used (0.1 W cm−2 ), the PL peaks at ~0.8 eV. With increasing excitation intensity, a continuous almost-parallel PL blue shift of 30–40 meV per decade of excitation intensity increase is observed. At an excitation intensity of 10 W cm−2 , the PL peak reaches ~0.92 eV. Under photoexcitation of 1–10 kW cm−2 , the low-energy part of the PL spectrum does not shift further, while the high-energy part continues shifting toward higher energy. Figure 2.20 compares PL spectra measured using a fixed excitation intensity (~5 W cm−2 ) at different temperatures in the range 8–210 K. These measurements clearly show that, with increasing temperature, the PL peak associated with SiGe clusters at 0.85–0.9 eV shifts toward lower photon energies. This “red” PL spectral shift is, most likely, associated with the SiGe band gap decrease as the sample temperature increases. Thus, it is opposite to the “blue” PL spectrum shift observed with an excitation intensity increase, and thus this blue shift cannot simply be explained by sample heating due to the intense incident laser beam (Fig. 2.22). There was some sample heating in the measurements, but it was not significant except at the higher laser powers. Using the observed broadening of the PL spectral features associated with c-Si, the sample temperature is estimated to rise from 4 to 60 K under the highest excitation intensity used. Figure 2.23 shows a modified (note the double logarithmic scale) Arrhenius plot of the normalized integrated PL intensity of a 3D Si/SiGe multilayer sample grown by CVD and measured at different excitation intensities. The normalized PL intensity temperature dependencies are fitted by a standard equation: 1   .   IPL (T) =  E1 1 + C1 · exp − kT + C2 · exp − EkT2

(2.1)

(see, for example, [41]) with two thermal quenching activation energies E1 and E2 . Here T is the temperature, k is the Boltzmann’s constant, and C1 and C2 are scaling coefficients. In all measurements of all samples, the PL thermal quenching activation energy E1 ≈ 15 meV and E1 is independent of excitation intensity. In contrast, the activation energy E2 depends significantly on the excitation intensity: the PL temperature dependence shows a step-like behavior, and E2 increases dramatically from ~120 to 340 meV as the excitation intensity increases from 0.1 to 10 W cm−2 . The PL dynamics, i.e., the PL intensity decay under pulsed laser excitation, is an important technique for studying the carrier recombination mechanism. Figure 2.24 shows the normalized low-temperature (T = 4 K) PL decays collected from a CVDgrown Si/SiGe 3D sample. The initial PL decay is fast—close to the resolution of our detection system (<20 ns). The longer-lived PL shows a strong dependence on the detection photon energy, as summarized in Fig. 2.25: the PL lifetime at photon energies below 0.8 eV is found to be ~20 μs, and it drastically decreases to ~200 ns for the PL component measured at 0.89 eV.

Three-Dimensional Silicon-Germanium Nanostructures

Fig. 2.23 Typical integrated PL intensity behavior for CVD-grown Si/SiGe 3D multilayer samples as a function of the reciprocal temperature measured with different excitation intensities, as indicated. The activation energies obtained from fits (shown by the different lines) to the data (shown by the different points) are also given

65

E1 ~15 meV, E2 ~150 meV

1

Normalized Integrated PL Intensity (arb. units)

2

E1 ~15 meV, E2 ~120 meV 2

0.1 W/cm 2 1 W/cm 2 5 W/cm 2 10 W/cm

0.1

E1 = 15 meV, E2 ~340 meV

10

100

1000/T (K–1)

0

T=4K

10 PL Intensity (arb. units)

Fig. 2.24 Typical low-temperature (T = 4 K) PL dynamics for CVD-grown Si/SiGe 3D multilayer samples measured at the indicated photon energies using a short (~6 ns) excitation pulse

0.77 eV

–1

10

–2

10

–3

10

0.83 eV 0.89 eV

0.86 eV

–4

10

0

10 Time (μs)

20

Carrier Recombination in Si/SiGe Nanostructures In our discussion of carrier recombination in Si/SiGe NSs, we focus on MBEand CVD-grown 3D (or cluster morphology) samples with an average Ge atomic composition close to 50%. These samples show the highest observed PL quantum efficiency (better than ~1% at low excitation intensity) with a PL peak wavelength close to 1.5–1.6 μm. The PL spectral distribution extending well below the band gap of pure Ge (Figs. 2.17 and 2.18) and the extremely long carrier radiative lifetime of ~10 ms [88], as well as the ~30 meV per decade PL spectral shift toward higher photon energies as the excitation intensity increases [102], point out strong

Fig. 2.25 Summary of PL lifetimes (T = 4 K) for CVD-grown Si/SiGe 3D multilayer samples at different photon energies

D.J. Lockwood and L. Tsybeskov

PL decay time (10–6 s)

66

101

100

10–1 0.78 0.81 0.84 0.87 PL photon detection energy (eV)

0.90

similarities between the PL in 3D Si/SiGe NSs and the PL in III–V quantum wells with type II energy band alignment [101]. Generally, a type II energy band alignment at the heterointerface is a strong disadvantage for light-emitting devices due to a weak overlap between spatially separated electron and hole wave functions. In reality, however, the critical limitation in the efficiency of light-emitting structures is rather the presence of competing non-radiative recombination channels for excess electrons and holes. The most important non-radiative mechanism is carrier recombination via defects, especially heterointerface structural defects such as propagating dislocations and dislocation complexes. The 3D Si/SiGe NSs investigated here, grown by both MBE and CVD processes, show an almost undetectable density of dislocations. Thus, in these properly grown 3D Si/SiGe NSs at low excitation intensities, we find a high quantum efficiency of PL with photon energy <0.9 eV, which is associated with carrier recombination in the vicinity of SiGe clusters. It has been suggested that SiGe Stranski-Krastanov (S-K) clusters with a small (3–5 nm) height and ~10:1 base–height aspect ratio can be modeled as NSs with a type II energy band alignment and possible SiGe cluster valence band energy quantization in the direction of growth [99]. Strained Si and Si-rich SiGe alloy regions near the base of the clusters (also called SiGe wetting layers) also need to be considered. Including the effect of strain, the observed PL bands at 0.916 and 0.972 eV indicate a composition of the Si1−x Gex transition region, which is located near the bottom of the Ge/Si pyramid-like clusters, to be close to x ≈ 0.2, and this conclusion is supported by recent direct analytical TEM measurements [90, 91]. It has also been proposed that the broad PL band with a peak energy of ~0.8– 0.9 eV is due to the recombination of carriers localized in the Ge-richest areas of the clusters, which is close to the center of “pancake”-shaped SiGe clusters [89]. We suggest that at the lowest excitation intensity, the PL arises from electron–hole recombination between holes localized in the Ge-richest regions of the cluster and electrons localized in the strained SiGe alloy region near the cluster base. This immediately explains the extension of the observed PL spectrum below the pure Ge band gap energy.

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The observed excitation-independent PL thermal quenching activation energy of ~15 meV is close to the exciton binding energy in SiGe alloys and Si/SiGe superlattices. Thus we conclude that one of the mechanisms of PL thermal quenching is the thermal dissociation of excitons. The activation energy of ~15 meV can therefore be associated with exciton localization on specific regions of the clusters associated with variations of the SiGe composition. Hence, the non-uniform SiGe cluster composition and, perhaps, variations in SiGe cluster size and shape could be responsible for the observed relatively broad PL spectra. Using the model discussed above of type II energy band alignment at the Si/SiGe heterointerface, we focus next on non-radiative carrier recombination and the different mechanisms of electron–hole separation. Electron transport in 3D Si/SiGe NSs is limited by a small (≤10−15 meV) conduction band energy barrier and SiGe compositional disorder [100, 103]. Thus, the PL thermal quenching activation energy of ~15 meV could also be associated with a small conduction band energy barrier for electrons in Si/SiGe 3D NSs. In contrast to a low-energy barrier for electrons, hole diffusion in 3D Si/SiGe multilayer NSs with a high Ge content is controlled by large (>100 meV) valence band energy barriers at Si/SiGe heterointerfaces. In this system, we consider two major mechanisms of hole transport: (i) hole tunneling and (ii) hole thermionic emission. Hole tunneling in 3D Si/SiGe NSs with thin (5–7 nm) Si-separating layers and nearly perfect SiGe cluster vertical self-alignment could be very efficient. These NSs are usually grown by MBE and exhibit a PL thermal quenching activation energy of ~60 meV. The same PL thermal quenching activation energy is found in our CVD-grown samples with 7.5 nm thick Si-separating layers for the lowest excitation intensity. We suggest that in 3D Si/SiGe multilayer NSs with thin Si layers at low excitation intensity, the electron–hole separation and non-radiative carrier recombination are mainly controlled by hole tunneling between SiGe clusters. Due to significant variations in SiGe cluster size, shape, and chemical composition, the process of hole tunneling could be assisted by phonon emission and/or absorption [102, 104]. Therefore, the observed PL thermal quenching activation energy is close to the Si TO phonon energy. In 3D Si/SiGe multilayer samples with 20 nm thick Si layers, where SiGe cluster vertical self-alignment is practically absent [89, 91], the probability of hole tunneling is reduced, and hole thermionic emission over the Si/SiGe heterointerface barrier plays a bigger role. Thus, in these samples the PL thermal quenching activation energy is expected to be greater, as has been found in our experiments (see Fig. 2.23). In this simple model, efficient hole tunneling between adjacent SiGe nanoclusters requires not only reasonably low and thin Si barriers but also a low carrier concentration (i.e., a large enough number of empty adjacent SiGe clusters). By increasing the photoexcitation intensity (i.e., the number of photogenerated carriers), hole tunneling can effectively be suppressed since fewer empty adjacent SiGe clusters can be found. At high excitation intensity, assuming (i) a negligible value of the conduction band offset compared to that in the valence band and (ii) a nearly pure Ge composition in the SiGe cluster core, the maximum anticipated PL thermal quenching activation energy should be E2 ≤ EgSi − EgGe ≤ 400 meV. This value sets the upper limit of the activation energy of PL intensity thermal quenching in 3D SiGe

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multilayer NSs, and it is close to the activation energy of E2 ≈ 340 meV that has been found under the highest excitation intensity (see Fig. 2.23). The same model also explains the experimentally found strong decrease in carrier radiative lifetime (~100 times) as the detection photon energy increases from 0.77 to 0.89 eV (Fig. 2.25). Under a low level of excitation intensity, holes are localized within the Ge-rich core of SiGe clusters, and the hole wave function does not penetrate into the Si barriers. Thus, in this quasi-type II energy band alignment, electron and hole wave functions do not overlap, causing a long carrier radiative lifetime. Under high-level excitation, holes occupying the excited energy states in small-size SiGe clusters, as well as holes leaking into the SiGe wetting layer with a lower Ge concentration, have their wave function significantly extended into the Si barriers. Therefore, a stronger overlap between electron and hole wave functions is responsible for a shorter radiative lifetime, i.e., a higher PL quantum efficiency at greater photon energy. Thus, this explanation is consistent with both the decrease of the PL decay time at greater photon energy and the PL spectral blue shift as excitation intensity increases. Figure 2.26 depicts the quasi-type II energy band alignment at Si/SiGe heterointerfaces, where a gradual increase of Ge concentration toward the SiGe cluster core has recently been experimentally verified (see Fig. 2.11 and also [91]). It also shows five major processes controlling electron–hole recombination in 3D Si/SiGe NSs with a Ge-rich core: (1) radiative recombination between electrons localized at the Si/SiGe heterointerface and holes localized within the Ge-rich core of a SiGe cluster—this slow recombination is associated with the lower photon energy part of the PL band; (2) radiative recombination between electrons localized at the Si/SiGe heterointerface and holes localized in excited states in small-size SiGe clusters as well as holes leaking into the Si-rich outer part of the cluster or/and SiGe wetting layer—this faster carrier recombination channel is responsible for the higher photon energy part of the PL spectrum;

Si

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Fig. 2.26 Schematic of the Si/SiGe cluster multilayer energy band diagram with different electronic transitions: 1—slow electron–hole recombination due to spatial separation and a weak wave function overlap; 2—a faster recombination, presumably involving holes at excited energy states in SiGe clusters; 3—hole diffusion due to cluster-to-cluster tunneling; 4—hole diffusion due to thermionic processes; and 5—Auger hole excitation with possible charge transfer

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(3) non-radiative carrier recombination due to electron–hole separation via hole tunneling in Si/SiGe NS samples with thin (<10 nm) Si barriers; (4) non-radiative carrier recombination due to electron–hole separation via hole thermionic emission in samples with thicker (>15–20 nm) Si barriers; (5) non-radiative carrier recombination due to Auger processes. It has been pointed out that possible transformations of hole energy spectra due to quantization and/or strain might dramatically increase the rate of non-radiative Auger recombination in SiGe quantum wells by more than 100 times [105]. Thus, the “Auger limit” in Si/SiGe NSs could be considerably lower compared to that in c-Si and c-Ge. On the other hand, the Auger process competes with radiative processes, and their characteristic lifetimes are ~ 10−3 s in bulk Si and Ge and just ~10−7 s in the high photon energy part of the PL spectra in 3D Si/SiGe NSs. More work is being done (see below and [56]) to understand the important details of Auger processes in Si/SiGe NSs. Figure 2.26 also reflects a continuous change in the Ge atomic concentration by a gradually increasing energy band gap from the cluster center toward the cluster edge and SiGe wetting layer where the Ge atomic concentration is estimated to be ~20%. The proposed energy band diagram and carrier recombination/diffusion mechanisms explain the experimental observations of (i) the PL spectral blue shift under increasing excitation intensity; (ii) the dramatic (~100 times) decrease in carrier radiative lifetime measured at photon energies from 0.77 to 0.89 eV; and (iii) the unusual PL intensity temperature dependence, which shows a different PL thermal quenching activation energy at different excitation intensities. This schematic representation also points out that moderate excitation intensity changes the overlap of electron–hole wave functions and allows a faster carrier radiative recombination. In other words, the type II energy band alignment at the Si/SiGe heterointerface can effectively be replaced by the “dynamic type I” alignment, where the electron and hole spatial separation no longer controls the recombination rate and the quantum efficiency of PL and EL.

Electroluminescence in Si/SiGe Nanostructures Electroluminescence (EL) in Si/SiGe NSs was demonstrated almost simultaneously with the first investigations of the PL [33, 99]. The structures used for the EL studies usually are Si/SiGe p-i-n diodes with SiGe clusters, SiGe alloy layers, or SiGe QWs in the i-region. Figure 2.27a shows EL spectra with quite narrow EL peaks attributed to NP and TO phonon emission [33]. The proposed EL mechanism is quite similar to the PL mechanism, i.e., it is due to radiative electron–hole recombination in Si/SiGe NSs with electrically injected electrons and holes. Similar to that in PL, the EL spectrum depends on the SiGe layer (or cluster) composition, and a higher Ge concentration results in the EL spectrum red shift (i.e., a shift toward lower photon energy). Figure 2.27b shows the dependence of the integrated EL intensity on current. The EL intensity versus current is a power function IEL ∼ J n where I is the

70 Fig. 2.27 (a) EL spectra of samples containing 3D SiGe NSs and (b) the EL intensity as a function of current under reverse bias. (Reprinted with permission from [33], Copyright 1995, American Institute of Physics)

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intensity, J the current density, and 0.5 < n < 2 [33]. A good-quality Si/SiGe p-i-n structure usually provides current flow associated with carrier diffusion in a forward biased p–n junction (i.e., an exponential current as a function of forward bias), and the diode ideal factor is less than 2 [33, 82, 106]. In Si/SiGe QW-based devices, the EL intensity temperature dependence, similar to that in PL, exhibits significant thermal quenching [33]. The EL thermal quenching activation energy is greater in Si/SiGe 3D nanostructures (especially with small-size SiGe clusters) compared to that in planar QWs, and the EL can be extended up to room temperature (Fig. 2.28) [106]. In [106], the EL thermal quenching activation energy is found to be as large as 200–250 meV, and this is, possibly, the largest reported value. The SiGe cluster EL spectra full width at half maximum is relatively narrow (~90 meV), possibly reflecting the cluster narrow size distribution. When the temperature increases from 40 K up to room temperature, the EL is reduced by a

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Fig. 2.28 (a) Room-temperature current–voltage characteristic of the p-i-n diode including one Ge hut cluster layer in the i-region. The device structure is given in the inset. (b) Temperature dependence of the EL spectra at constant current of 400 mA. (Reprinted with permission from [106], Copyright 2003, American Institute of Physics)

factor of ~40, but the EL peak is still observable at approximately the same photon energy. Considering the EL mechanism, the luminescence efficiency is believed to be limited (similar to that in PL) by type II radiative recombination between holes confined in the SiGe clusters and electrons localized in the silicon spacer layers above and below the islands. Also in the p-i-n structures with 3D Si/SiGe layers within the active region, the series resistance is found to be high (Fig. 2.28). Thus, the EL power efficiency is low, in part due to the high series resistance of the Si/SiGe p-i-n diode. Typically, as already mentioned, for a current density of 1–100 A cm−2 , the EL intensity is a power function of current IEL ∼ J n with 0.5 < n < 2. Thus, in p-i-n structures, the EL intensity should have an exponential dependence on the applied forward bias. In a simpler structure with two nearly ohmic contacts to Si/SiGe cluster multilayers, the integrated EL intensity is found to be nearly linear as a function of the applied voltage (Fig. 2.29). There are no energy barriers due to the p-i-n junction in these samples, and the EL intensity as a function of temperature shows thermal quenching with a smaller activation energy of ~130 meV (Fig. 2.30a). Interestingly, in the same sample, the device current as a function of temperature shows nearly an exact anti-correlation with the EL intensity and exhibits an activation energy of ~140 meV (Fig. 2.30b). Since both carrier transport and EL intensity exhibit a strong dependence on temperature, an accurate estimation of the EL quantum efficiency over a wide temperature region requires normalization of the EL

72

30 Integrated EL intensity (a. u.)

Fig. 2.29 Integrated EL intensity over the 0.75–0.95 eV spectral region for a CVD-grown Si/SiGe 3D multilayer sample as a function of the pulsed voltage amplitude measured at the indicated temperatures. The dashed straight line is a guide to the eye

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intensity on current density, i.e., measurements of how many photons are emitted per one injected electron–hole pair at different temperatures. The importance of the last statement is pointed out in [107], where the EL of light-emitting diodes with 5, 10, and 30 layers of Si/Ge clusters in the active region is studied. The enhanced integral EL intensity at temperature T ≥ 200 K in the samples with 30 layers of Si/Ge clusters presents a behavior opposite to the usually observed EL intensity thermal quenching, which is also found in the similar samples with 5 and 10 Si/SiGe layers. In [107], this EL intensity temperature dependence is attributed mainly to the EL intensity dependence on injection current, which according to Fig. 2.30 is temperature activated.

Photoluminescence in Si/SiGe Nanostructures Under High Excitation Intensity Figure 2.31 shows PL spectra of 3D Si/SiGe nanostructures measured under different levels of photoexcitation [56]. Using relatively low (≤1 W cm−2 ) CW excitation, a broad PL feature is found at 0.75–0.9 eV, which is associated with SiGe clusters, together with a much weaker PL peak that is associated with Si exciton recombination at 1.096 eV. On increasing the excitation intensity there is a rapid saturation of the SiGe cluster PL. Under pulsed excitation of ~6 ns duration and an energy density of ~0.1 mJ cm−2 , which corresponds to a nearly ~1,000 times higher peak intensity, SiGe cluster PL becomes negligible compared to Si PL. At the same time, a broader PL peak at 1.079 eV appears. When the excitation intensity approaches 10 mJ cm−2 , this broad PL peak shifts to a slightly higher photon energy (~1.085 eV), and it quickly becomes the dominant PL feature (see Fig. 2.31). We find that the intensity of this PL band as a function of excitation intensity follows the dependence

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Fig. 2.30 (a) The EL intensity and (b) current as functions of the reciprocal temperature for a CVD-grown Si/SiGe 3D multilayer sample. The activation energies obtained from fits to the data (dashed lines) are also shown

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IPL ∼ (Iexc )n , with n ≈ 1.2−2, and it anti-correlates with the SiGe cluster PL where n correspondingly varies from 0.8 to 0.5. This faster growing, broader PL band is associated with the recombination of Si electron–hole condensates or electron–hole droplets (EHDs).

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Fig. 2.31 The PL spectra in 3D Si/SiGe nanostructures at 15 K measured under CW excitation with intensities of (1) ~1 W cm−2 and (2) ~100 W cm−2 ; and under pulsed excitation with 6 ns pulse duration and energy densities of (3) ~10−5 J cm−2 , (4) ~10−3 J cm−2 , and (5) ~10−2 J cm−2 . The PL spectra are shifted vertically for clarity, and PL peaks associated with SiGe clusters (SiGe), Si free excitons (FE), and Si EHDs are indicated. The inset shows a dark-field cross-sectional TEM micrograph with SiGe clusters as lighter areas separated by ~10–15 nm thick Si layers

Figure 2.32 shows low-temperature PL dynamics in a high resistivity (≥104 ·cm) bulk c-Si sample and focuses on Si exciton recombination at 1.096 eV and Si EHD recombination at 1.079 eV. There is a dramatic difference in the PL decay lifetimes, changing from ~3 μs in Si exciton PL to ~70 ns in Si EHD PL. For this

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Fig. 2.32 Low-temperature PL dynamics in a bulk c-Si sample under 0.1 mJ cm−2 energy density excitation recorded at photon energies associated with the Si FE and Si EHD PL bands

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Fig. 2.33 The PL dynamics under pulsed laser energy densities of (a) 0.1 and (b) 10 mJ cm−2 recorded at photon energies associated with SiGe cluster PL (~0.82 eV) and Si EHD PL (~1.08 eV)

excitation intensity, both PL decays are nearly a single exponential. The PL rise time in c-Si EHDs is faster than the experimental time resolution of ~2 ns, while in c-Si exciton PL the rise time is ~20 ns. Figure 2.33 depicts low-temperature PL dynamics in 3D Si/SiGe nanostructures, focusing on SiGe cluster PL (measured at photon energy 0.82 eV) and Si EHD PL with a peak at ~1.08 eV. The PL associated with SiGe clusters rises practically instantaneously, while the PL associated with Si EHDs, in contrast to that in bulk c-Si (Fig. 2.32), has a slower rise time of ~20–40 ns. For an excitation energy density of 0.1 mJ cm−2 , the SiGe cluster PL decay is non-exponential, with a fast initial characteristic lifetime of ~20 ns followed by a much slower (τ ≥ 10−4 s) decaying PL. At the same time, the Si EHD PL has a nearly single exponential decay with a lifetime τEHD ∼ 50 ns (Fig. 2.33a). Using a 100 times higher excitation intensity, there is an acceleration of the fast component of SiGe cluster PL decay surprisingly followed by a non-monotonic, at first rising and then falling (i.e., N-shape), PL signal (Fig. 2.33b). Under the same excitation conditions, the Si EHD PL exhibits a nearly exponential decay with a lifetime of ~200 ns followed by a very fast (faster than 20 ns) decay (Fig. 2.33b). The Si exciton PL dynamics in Si/SiGe 3D nanostructures, like that in bulk c-Si, is much slower, with a microsecond characteristic lifetime. Assuming a quasi-type II energy band alignment at Si/SiGe heterointerfaces (see Fig. 2.34), we propose that a 3D Si/SiGe nanostructure can be represented by a coupled electronic system, where Auger recombination in SiGe clusters not only is responsible for the fast saturation of the SiGe cluster PL intensity but also injects “Auger holes” into the Si nanometer-thick layers. This process facilitates the formation of Si EHDs. Thus, compared to bulk c-Si, where at an excitation energy density of ≥0.1 mJ cm−2 EHDs are formed practically instantly from hot electron–hole

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Fig. 2.34 Schematic representation of recombination processes in a Si/SiGe 3D nanostructure. (a) At low excitation intensity, because of the long carrier radiative lifetime in Si energy barriers, a hole falls into a SiGe energy well and recombines with an electron localized in Si. (b) At high excitation intensity, the “Auger fountain” ejects holes from SiGe clusters into Si layers and facilitates the formation of Si EHDs. The fast Si EHD recombination becomes the dominant recombination mechanism

plasma condensation, in Si/SiGe 3D nanostructures Si EHD formation is mediated by the Auger processes with a characteristic time of ~10−8 s. At low excitation intensity, the Si electron–hole density is too low for EHD condensation and Si carrier recombination is slow. Under these conditions, photogenerated holes created in Si would rather fall into SiGe clusters. Thus, assuming a defect-free Si/SiGe heterointerface, slow radiative recombination between spatially separated electrons and holes at the Si/SiGe heterointerface is the only possible channel of radiative recombination. This conclusion is supported by the spectra given in Fig. 2.31, which show a dominant SiGe PL band only at low excitation intensity. At a high level of photoexcitation, SiGe Auger recombination overcomes the slow recombination of spatially separated electrons and holes at the Si/SiGe heterointerface (i.e., an indirect exciton). This process generates “Auger holes” with energies of 0.7–0.8 eV, while the valence energy barrier at the Si/SiGe heterointerface is <0.3–0.4 eV, and thus the fast Auger hole injection from SiGe clusters into Si barriers can be very efficient. The Auger-mediated hole transfer from SiGe clusters into Si barriers not only suppresses the SiGe cluster PL but also contributes to carrier accumulation in the nanometer-thick Si-separating layers resulting in EHD condensation. The EHD condensation from the electron–hole–gas is a first-order phase transition, and it depends on the excess carrier concentration and temperature. According to our data (Fig. 2.33b), it takes ~10−6 s after the short laser pulse for the carrier concentration to drop below the EHD condensation threshold and for the reverse EHD/electron–hole–gas phase transition to take place. This reverse phase transition creates recombination conditions very similar to that at low excitation intensity. Thus, instead of waiting a long time to recombine with an electron, a hole located in the Si barrier would be quickly recaptured by the SiGe cluster, where it will eventually recombine with an electron in Si. This hole capture by SiGe energy wells explains the observed rise (after ~10−6 s) in the SiGe PL intensity (Fig. 2.33b). The longer time (>10−6 s) part of the SiGe PL decay is governed by the continuously decreasing SiGe cluster carrier concentration.

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SiGe Light Emitters: Integration Issues and Compatibility with CMOS Besides the challenges associated with Si/SiGe nanostructure luminescence efficiency, speed, and thermal quenching, another critical question is their potential compatibility with the standard CMOS process. Fortunately, Si/SiGe technology, specifically SiGe heterojunction bipolar transistor (HBT) technology, is quite mature, and full SiGe heterostructure BiCMOS production lines were introduced in the late 1990s [69]. At that time, the most important issue in the HBT device design was not the individual device performance but rather the integration of the SiGe transistor into the standard silicon process with the minimum of additional cost. It was anticipated and later proved that the major increase in cost was the addition of SiGe epitaxy to the existing CMOS process: Several estimates showed that the cost increase was close to ~10%. Numerous new applications of SiGe transistors have emerged almost immediately, including advanced analog-to-digital converters and radiofrequency (RF) devices for local and world area networks. Indeed, the relatively recent explosive growth of wireless systems at the marketplace is proving that this investment provides a very high return. Assuming that the technical problems with Si/SiGe light emitters can be solved, can “opto-CMOS” repeat the success of BiCMOS and RF-CMOS? This question has been discussed in several early publications and in more recent papers including some published in a recent special issue of the Proceedings of the IEEE [108]. In early publications, the ambitious goal of creating a new computational environment is well summarized in Fig. 2.35, where Si/SiGe nanostructures are used in a variety of “high-end” electronic and photonic devices including unspecified quantum devices, resonant tunnel

Fig. 2.35 Schematic of the suggested system-on-a-chip incorporating Si/SiGe nanoheterostructures with new functionalities as opposed to those of traditional CMOS. (Reprinted with permission from [69], Copyright 2004, Institute of Physics)

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(a) (b) 0.7 µm

Fig. 2.36 (a) Schematic and (b) SEM view of selectively grown SiGe light emitters with the specified dimensions. (Reprinted with permission from [109], Copyright 1997, American Institute of Physics)

diode memories, high-index waveguides, modulators detectors, and even lasers [69]. This revolutionary approach will most likely require an enormous investment in the fabline infrastructure with a possible payoff in the quite distant future. Another, more conservative (or “evolutionary”) approach considers limited applications of integrated optical interconnects, mainly for on-chip communication involving processing and transmission of relatively high volumes of data [108]. Also, the choice of the SiGe light emitter design is not currently clear (planar, vertical, directly integrated into a high-index waveguide, etc.). Figure 2.36 shows a proposed device design based on selective epitaxial growth using a lithographically defined SiO2 mask and emphasizes a large device surface area [109]. Will the extremely high cost of the “wafer real estate” allow this particular device geometry? The answer, most likely, is “no.” Also, in order to be combined with a high-index waveguide and a high-speed photodetector with minimum possible losses, all devices should probably be grown within the same processing step, and that requirement creates additional technological problems discussed in several review papers [17, 110–113].

Conclusion In conclusion, the basic light-emitting properties of SiGe nanostructures have been reviewed with a major focus on new developments in 3D Si/SiGe NSs. These NSs emit light at the technologically important 1.3–1.6 μm wavelength region, and the highest PL and EL quantum efficiency is found in SiGe clusters with a ~50% Ge composition near the cluster core. A high luminescence quantum efficiency is observed at low excitation intensity, and the PL quantum efficiency decreases as the excitation intensity increases, most likely due to competition with faster non-radiative Auger recombination. Using time-resolved PL measurements, it has

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been found that within the broad PL band, the part of the PL spectra at higher photon energies exhibits a ~100 times faster radiative transition, which is explained by a proposed model where radiative recombination occurs between holes (occupying excited states in SiGe clusters and/or outer, i.e., Si-rich, portions of SiGe clusters) and electrons mostly localized at Si/SiGe interfaces. This fast PL is less susceptible to Auger-induced intensity saturation as the excitation intensity increases. In addition, this PL exhibits an improved intensity temperature dependence: the PL can easily be extended up to room temperature. It has been shown that the EL in Si/SiGe nanostructures is very similar to the PL in its physical nature and that it can also be extended up to room temperature. In 3D cluster morphology multilayer Si/SiGe nanostructures, an anti-correlation exists between the PL originating from SiGe clusters and the PL associated with EHDs localized within nanometerthick Si-separating layers. Auger processes eject holes from the SiGe clusters and facilitate the exciton/EHD phase transition in the Si layers. The Si EHD lifetime is less than 10−7 s and at high excitation intensity this is the dominant recombination channel. These experimental observations suggest that by controlling and modifying the composition of Ge-rich SiGe clusters (and possibly other types of Si/SiGe 2D and 3D NSs) it is possible to fabricate a more efficient SiGe light-emitting device. Despite the previously discussed challenges associated with integration into the traditional CMOS environment, the proven compatibility between Si/SiGe and conventional CMOS technology suggests that this task is not an impossible one. Acknowledgments We would like to acknowledge the invaluable contributions over a number of years from our many collaborators on this work and whose names are given in the references to our work in this chapter and thank especially B. Kamenev of NJIT, J.-M. Baribeau and X. Wu of NRC Canada, and T. Kamins of HP Laboratories. We acknowledge the partial financial support for this research provided by US National Science Foundation, Intel Corporation, Semiconductor Research Corporation, and Foundation at NJIT.

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Chapter 3

On Application of Plasmas in Nanotechnologies Zoran Lj. Petrovi´c, Paul Maguire, Marija Radmilovi´c-Radjenovi´c, Maja Radeti´c, Nevena Puaˇc, Dragana Mari´c, Charles Mahony, and Gordana Malovi´c

Abstract In this chapter we give a review of the application of non-equilibrium plasmas in the field of nanotechnologies, and nanotechnology-related science. The field of applications of plasma in general in nanotechnologies is extensive, and the field of non-equilibrium plasmas in the same context is almost as large with many possibilities covering both top-down and bottom-up fabrication approaches. Thus a single review cannot give it justice. We opted here, as may be expected, to give a review of possibilities in general, ranging from the growth and functionalization of aligned nanotubes, carbon walls and sheaths of graphene, through to the growth of gas-phase nanocrystals and dust particles; surface deposition of different structures, functionalization of the surface and conditions for developing means to prepare hyperhydrophobic surfaces; treatment of textiles, organic materials, living cells, to applications in nanoelectronics for the manufacture of future generations of integrated circuits to meet the Moore’s law driven semiconductor roadmap. In a text like this it is not possible to cover all issues and even less to cover all sources. We thus focus on several topics and mostly on the plasma physics problems related to improving the plasma technologies. They include charging as a source of errors in integrated circuit fabrication to the generation of non-equilibrium plasmas at atmospheric pressure for even more convenient application and for applications in biomedicine. The message we hope to convey to all readers is an understanding as to the explicit advantages that non-equilibrium plasmas have in a large number of plasma-assisted nanotechnologies and other modern technologies—an advantage that other emerging technologies will struggle to match at the levels of integration, cost and quality required of future fabrication.

Introduction Micro- and nanofabrication are important in many areas of modern economy, trade, science and technology and a lot of effort has been devoted to fabricating smaller Z.Lj. Petrovi´c (B) Institute of Physics, University of Belgrade, POB 68, 11080 Zemun, Serbia e-mail: [email protected] A. Korkin et al. (eds.), Nanotechnology for Electronics, Photonics, and Renewable Energy, Nanostructure Science and Technology, DOI 10.1007/978-1-4419-7454-9_3,  C Springer Science+Business Media, LLC 2010

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and smaller patterns [1–4]. Nanotechnology (from the point of view of applications in electronics) seems to be nothing more than an extension of the micro-electronics technology, a step further towards miniaturization. On the other hand, nanotechnology is expected not only to reduce the dimensions of the existing microdevices, but, more importantly, to produce objects and materials with fundamentally different (new) properties and capabilities [5–7]. The expectations of what nanotechnology will achieve in the future range from quantum computers, ultra strong materials, self-cleaning fabrics and information storage and retrieval to drug delivery to individual cells and to implantable biosensors [8–14]. Nanotechnologies appear to be the current buzzword across a number of disciplines supported by policies of science funding agencies and editors of scientific journals. The field was certainly a novelty in science which, after a long and broadly focused initial period, bloomed when the numbers of scientists working in that field reached critical mass for a publication explosion. As the novelty is wearing off, the focus on research supporting the most promising applications is becoming a priority. This in turn increases the importance of plasma technologies related to the nanoscience and especially nanotechnologies. These two are often identified although they differ considerably. While we could define nanoscience as the science about miniscule objects that belong in general to the nanometre world, the nanotechnology should consist of techniques that allow us to organize nanosized objects in predictable and eventually useful fashion. The nanotechnology also includes the relevant science to achieve these goals. There is a considerable difference between the two meanings. While plasmas could perhaps present a borderline case for belonging to the former group the case for belonging to the latter group is very strong, perhaps even essential. The situation is in a way similar to the micro (nano) electronic devices. While the physics of these devices does not require plasma physics, the main reason for their success lies in continuous miniaturization which not only increases the power of the existing devices and integrated systems but also opens new possibilities, products and markets. Some of the key processes in the miniaturization and production of integrated circuits are closely related to plasma physics (plasma etching, plasma cleaning, implantation). As a matter of fact we may regard the combination of photolithography and plasma etching as the standard technology for producing integrated circuits. The connection of nanotechnologies and plasmas is even stronger as the discovery of some of the critical nano-objects occurred in plasmas [15–17]. Nevertheless, in order to justify the presence of plasmas within nanotechnology projects, conferences and strategies and priorities in science, one of the authors of this text had to resort to citing an old nursery rhyme about seven blind men who went to India to see an elephant. Each touched one part of an elephant and came to a conclusion about the elephant limited by his experience. None had seen the whole truth. In a similar fashion scientists tended to see nanotechnologies only through their own scientific interests and viewed other lines of research as less relevant or as a competition. Luckily, with the focus on practical applications being dictated by funding agencies, methods are sought that can bridge the gap between experiments with individual building blocks and massive, parallel production. In that respect plasmas

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are viewed as one of the best possible methods to bring together nanoscience and nanotechnologies with industrial production. This may be associated with the continuous progress in the standard technology of integrated circuits which, having mastered the 45 nm resolution, is progressing further to 32 nm and even higher resolutions (it has been reported that 32 nm production has begun this year). These technologies are developed as a complete set of processes to operate under industrial environment and to produce economically viable products. Thus the standard micro-nano electronic technology is a true nanotechnology developed all the way to the industrial level. More about that later on. Two paradigms define the further development of nanotechnologies. The bottomup approach is based on using the best of our abilities and facilities to produce some structures with extremely small dimensions, even at the level of single atoms, in fact to tease out the self-building properties of materials and structures. The aim is to use those structures as the building blocks of larger devices or materials. While that approach is based on major achievements in terms of human abilities, an even more challenging step will be to transfer this ability into industrially applicable and economically viable technology. For example, if we were able to develop a transistor that has a miniscule size equal to one molecule and we are able to put it on a surface in a precise position and prove its functionality we are still far from a useful technology. We need to put one billion transistors like that, in a short time, and to connect them in such a way that the whole system functions as a well-defined integrated circuit (IC). In order to keep up with the existing technology of integrated circuit production, all that should cost only a few hundred dollars per IC. It is thus obvious that the critical research in this approach will be not only in achieving a basic result but also in providing the technology for its practical implementation. The second approach is to follow the path set out by Moore’s law (more than 40 years ago) [18] and by the roadmaps outlined by the micro-electronic (now already nanoelectronic) industry. That is to carve the final product in a block of material where one may follow the existing and well-proven technologies and to allow them to achieve further miniaturization through research requiring a large degree of ingenuity. The latter approach is the strategy of the so-called top-down technologies. While the bottom-up approach is in the domain from 1 nm to 10 nm, it is not yet well established in industrial applications. The top-down approach is at the moment at 45 nm (with recently introduced 32 nm production) in mass production while 22 nm technology is just round the corner. One is left with the research for future incarnations of miniaturized technologies. Those will, no doubt, require changes in the basic principles as well as in the materials that are used. On the other hand, one should be aware of the inertia of the industry whose favourite at the moment is definitely silicon substrate with the standard production technology. Another issue is to maintain the growth of the associated industries that feed the research and further advances. While having in mind the holy grail of the modern applied research in physics is to maintain Moore’s law, we can safely predict that most of the research that is carried under the banner of bottom-up nanotechnology

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will actually yield applications in completely different, still unforeseen, areas. Yet both bottom-up and top-down technologies have to feed the support for the advances in electronics-related applications. One should thus bear in mind that the ICs of the near and not so near future will still be made by using the same principles that are implemented today and will include the two steps that are critical for further miniaturization: photolithography and plasma etching. Whatever the approach, plasmas, in particular the low-temperature plasmas, will have a large role to play in bringing the technologies from the scientific laboratories to mass production. While that may be expected in the top-down approach the bottom-up achievements may also need plasma processing, in particular plasma growth of nanostructures on surfaces and in gas phase for achieving self-organized and functional assembly of nanostructures in industrial environment. In many ways plasmas are ideal for creating and allowing self-assembly of the building blocks in the bottom-up approach. In this chapter we shall give a review of the application of plasmas in nanotechnologies. After briefly discussing the broader field we shall focus and give examples from the realm of our interests and experience. In other words, this would be just a report of one blind group that attempted to represent the big picture from its narrow and focused experience. Even the field of application of plasmas in nanotechnologies is too vast for one group of similarly minded people to represent. The need to inform a wider audience and the limited space mean that in some cases the coverage will be too brief and even trivial for specialists.

Introduction to Plasma Physics and Why Plasmas Are Useful In a low-pressure gas, plasma is produced by the dissipation of electrical power to the gaseous medium. Electrons, to which most of the power is transferred, gain enough energy to initiate, in collisions with atoms and molecules, processes such as excitation, ionization and dissociation. Atoms, radicals and ions, which are produced this way, are at the origin of further reactions and, as a consequence, the plasma phase is generally a very complex mixture of chemical species [19]. Ultimately, the plasma species interact with the walls. Adsorption of species will occur depending on the chemical affinity and surface temperature. Adsorbed species may react with the surface to form a product or desorb without or after a surface reaction. If the product is volatile, it will desorb into the plasma phase and cause etching (removal) of the material from the surface. The material will either be eliminated through pumping or participate in the plasma chemistry. If the product is not volatile, it will contribute to the formation of a thin film at the surface. Ions, electrons and photons also interact with the surface. In plasma processing, the sample is, in general, negatively biased with respect to the plasma by means of the external power supply, so positive ions play a very important role in plasma surface interactions. Ions bring energy to the surface and, thus, can assist chemical reactions and desorption of weakly volatile species, or induce direct sputtering.

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Plasmas are well defined in physics as gases with a large number of free electrons and ions that may be able to gain energy from the external electric fields and that satisfy certain criteria [20, 21]. One is that the size of the plasma should exceed other characteristic lengths such as the mean free path between collisions and the Debye length, the other is that they are quasi-neutral. In principle, plasmas maintain their prescribed electroneutrality by protecting themselves through generation of strong fields (in narrow volumes at their edge, known as sheaths) from the vessel that contains them (which is presumably a solid-state material that may be grounded if it is conducting). While one can often hear about non-neutral plasmas or even singlecomponent plasmas, those are systems that are similar to plasmas (that follow the standard definition) due to strong coupling through Coulomb interaction of charged particles. Ionized gases are not defined as narrowly as plasmas and merely are gases with free charged particles and without any specific conditions. The definition encompasses very weakly ionized gases that are also known as ‘swarms’ of charged particles (ensembles of independently moving charged particles driven by external field and collisions with the unperturbed molecules of the background gas), gas discharges (where charged particle densities may become sufficient to affect the distribution of the external electric field) and plasmas. As the charged particle density increases, properties of the ionized gas change dramatically. Two types of plasmas (and in broader sense ionized gases) may be defined. Those with lower densities of charged particles are known as the so-called non-equilibrium plasmas or low-temperature plasmas (sometimes even cold plasmas). When charged particle densities are higher usually one has equilibrium or thermal plasmas. In non-equilibrium plasmas one uses the great mass ratio between electrons on one side and positive ions and background gas molecules on the other to decouple transfer of energy to electrons by electric field from the subsequent transfer of kinetic energy to ions and molecular particles. Thus electrons may achieve high energies and start dissociation and ionization while at the same time ions in the bulk of the plasma have low mean energies. This property of non-equilibrium plasmas is often described through the relation Te >> Ti = Tg , where the respective temperatures of electrons, ions and gas molecules are a representation of their mean energies. Under the non-equilibrium conditions under discussion, the temperature of electrons, and even ions, are not well defined since the energy distribution function may be quite complex and different from a Maxwellian distribution, typical of gases [22]. Thus to sum up the intrinsic property of the non-equilibrium plasmas is that the energy from the external field may be transferred efficiently to electrons which initiate collisions leading to ionization to maintain plasma and dissociation which leads to a very reactive environment but that gas molecules and ions have low energies, which allows plasmas to treat thermally unstable materials including polymers, organic materials and even the living matter. When charged particle densities become sufficiently high, Coulomb interaction couples electrons and ions more strongly and there is sufficient energy transfer between the two groups so that some of the energy gained by electrons is transferred to ions. Eventually their temperatures will become identical. At the same time ions

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can transfer their momentum to the gas molecules so the energy eventually ends up in heating of the gas and the walls of the chamber. For the same given mean energy, thermal (equilibrium) plasmas are much more efficient in producing radicals (if the mean energy is sufficient). However, overall when total energy input is taken into account, non-equilibrium plasmas have a greater efficiency in using the energy as one may choose conditions so that electrons have a very high probability for a given process and at the same time no energy is wasted in heating of the gas and vessel. Thermal plasmas are described by one parameter only, their temperature. Yet one could claim that only for the first 200,000 years of the universe did equilibrium plasma exist. We can, however, find numerous examples when plasma may be described by temperature albeit one that is variable across the plasma profile. In other words, those plasmas are not truly in equilibrium, and temperature is only useful in describing the properties locally. Spatial variation of the effective temperature reveals the degree of non-equilibrium. These temperature profiles are usually determined from spectroscopy, and to justify a claim for any degree of equilibrium, the temperature should be the same for all possible combinations of excited states (for the given position). If those temperatures, at a certain point, vary depending on the energy levels and processes, that is the sign of non-equilibrium. One usually does not calculate the plasma temperature from first principles; the temperature is a fitting parameter for a series of measurements. One of the essential differences between equilibrium (thermal) and nonequilibrium (low-temperature) plasmas is in the fact that in the latter case individual collisional processes may change the electron energy distribution function (EEDF) considerably [21]. From a ‘half empty glass perspective’ we can consider this a problem; our optimistic ‘half-full’ interpretation is that we now have an opportunity to design the EEDF to fit the desired requirements. Adding a small amount of some gas with specific processes may achieve that goal, both by the shape of the cross sections and/or by getting the plasma to operate at a different E/N (electric field normalized to the gas number density usually given in units Townsend, 1 Td = 10−21 V m2 ). Thermal plasmas, on the other hand, are to a large degree insensitive, even to the main buffer gas, as their properties would be similar for different gases, even for rare and molecular gases. These distinctions may certainly be observed in spectroscopy. There are plenty of plasmas where theory developed for equilibrium plasmas apply to the non-equilibrium case albeit with the use of an effective temperature that may be spatially dependent. In those plasmas the temperature is measured rather than derived from the energy balance. Spatially dependent effective temperature with local thermodynamic equilibrium (LTE) has all the properties of equilibrium plasmas even though their properties may not be uniform. Indication of a non-equilibrium nature would come from very different effective temperatures measured for different processes. For example, vibrational and rotational temperatures in most gas discharges may be few thousand degrees and few hundred degrees, respectively. This is an indication that temperature is a poor representation of all processes, even individual processes, and that EEDF may be quite different from a Maxwellian distribution.

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Both low-temperature and thermal plasmas are being used in nanotechnologies, each with its own advantages and range of applications. Thermal plasmas were originally associated with the discovery of some of the key nanostructures, fullerenes and nanotubes. Discovery of the fullerenes [23] was made, in the ‘one person’s garbage is another person’s Nobel prize’ fashion, in the dust created by arc plasmas [24]. On the other hand, non-equilibrium discharges have been associated with anisotropic etching, as discovered empirically by Hosokawa in the early 1970 s [25], and these are becoming more and more important for nanotubes and nanocrystals since they provide a better control of properties of the created nanostructures. Thermal plasmas are definitely more productive if large quantities are required, but at the same time they are much more costly in terms of energy invested as most of the energy goes to heat the chamber and the background gas. Non-equilibrium plasmas, on the other hand, may have a very efficient use of energy as one can have most of the energy used up by electrons. In addition, by tailoring the process one may even have a reasonably productive process or a very specific process with fine tuning that cannot be achieved in thermal plasmas. At the same time nonequilibrium plasmas, if used properly, have advantage for treatment of materials (and living tissues) that are sensitive to high temperatures. Non-equilibrium plasmas are easily produced at low pressures (around 1 Torr) and under those conditions one may achieve large volumes, great uniformity and easily controllable properties. At high pressures, however, the ionization rate becomes quite high thereby producing large quantities of charged particles in a small distance crossed by charged particles. Thus thermal equilibrium plasmas are generally created. In order to achieve non-equilibrium operation of plasma at elevated pressures one needs to interrupt the charged particle production in some way and limit it. It can be achieved in very inhomogeneous fields where breakdown condition is satisfied only in a very small volume (corona discharges), by spatial interruption of the field with an inserted dielectric barrier where charges from plasma are deposited and may shield the field (dielectric barrier discharges), by high-frequency fields or localized microwave plasma production in a flow of rare gases mixing with the atmosphere or sometimes even in air. Finally, as the optimum gap for breakdown at 1 Torr is 1 cm, non-equilibrium operation at atmospheric pressure of around 760 Torr may be achieved with very small discharges with gaps of the order of 100 μm or less. Achieving flexibility and the ability to tailor the process and treat thermally sensitive targets, while still being able to operate at atmospheric pressure, is one of the holy grails of plasma physics, and all aspects of atmospheric pressure non-equilibrium plasmas are of primary interest for research and applications at the moment. To some degree blinded by our interests and the need to cover mainly the technologies for electronic devices, we shall focus here on non-equilibrium plasmas, even though thermal plasmas are also of great interest for nanotechnologies. In addition, we shall only cover the technology itself briefly and devote more space to fundamental issues in plasma physics that need to be solved or optimized further. To summarize, one may view plasmas as a source of free radicals, charges

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with different energies and ability to affect surface and basis and support for numerous gas-phase and surface chemical reactions. It can all be tuned and optimized but sometimes the parameter space is just too large and often empirical developments yield the best results. Nevertheless, with highly specific and technical requests of the current technological needs, a full understanding of plasma kinetics is required to optimize reactors.

Plasmas for Manufacturing of Integrated Circuits Plasma Etching in Nanoelectronics The physical basis for application of plasmas in IC manufacturing arises from the reactive ion etching (RIE) which was observed empirically by Hosokawa and coworkers in [25]. This empirical discovery led to significant advancement of microelectronics even before it was explained through direct experiment in 1979 [26]. In Fig. 3.1 we show a schematic representation of physical etching by Ar+ ions and chemical etching by XeF2 reactive molecules from [26]. The combined effects are at least 10 times faster as the two processes show a large degree of synergism. Application of the non-equilibrium plasma requires that the mean energy of ions in the bulk of the plasma is low (close to thermal) and ions gain most of their energy in the sheath. Thus their trajectory is perpendicular to the surface of the wafer, allowing a high degree of anisotropy if the process is activated by high-energy ions. Properly chosen plasma chemistry will produce a large density of highly reactive radicals that cover all the surfaces and etch much faster if activated by high-energy ions. At the same time, selectivity of etching is achieved with a proper choice of

Fig. 3.1 Schematic representation of the synergism between reactive and physical etching by combined effects of XeF2 reactive molecules and high-energy ions

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radicals whereby a great difference in the etching rate exists between the mask (photoresist) and the substrate (poly-Si or SiO2 ). We may, however, state that the property of the non-equilibrium plasmas that the ions are at the room temperature while the electrons are at a much higher effective temperature (mean energy) is the basis for anisotropic etching that has enabled emergence of submicron technologies and has fuelled the growth of electronic industry for the past three decades according to the Moore’s law [18]. Plasmas used for etching invariably operate at radio frequencies between 13.56 MHz and 200 MHz and in recent years two modes of operation have become dominant: capacitively coupled plasmas (CCP) and inductively coupled plasmas (ICP). Plasma sources may also be enhanced by application of external magnetic fields. In principle, using reactive chemicals or thermal plasmas would lead to production of an isotropic etch as under equal temperatures directions and energies of all active particles, ions and radicals would be evenly (isotropically) distributed (see Fig. 3.2) over the surface. The isotropic etch is not sought as it reduces the resolution to a much larger value than that defined by photolithography and also it does not allow high aspect ratios (ratio of depth to width) of plasma-etched structures. In addition, under those conditions the very high energies required to initiate efficient anisotropic etching of some materials such as SiO2 are not available. As mentioned above and as shown in Fig. 3.3, in non-equilibrium plasma the radicals are distributed evenly while, in the high field of the sheath, electrons that start from the plasma with a relatively high energy slow down and barely reach the surface while ions are accelerated from the thermal (room temperature) energy and reach the surface with high directed energy and velocity and at right angle to the surface. High fields generated in the sheath and by the bias voltage add the possibility to adjust the energy to activate efficient etching in some materials. For example SiO2 requires few hundreds of electron volts of energy per ion. Etching is a much more complex process, involving redeposition, polymerization and charging of the dielectrics. In addition, ions and UV photons originating from the discharge deposit most of their energy deep inside the substrate which may lead to the damage of the substrate. Damage may also occur due to charging of

Fig. 3.2 Isotropic etch as a result of liquid chemical or thermal plasma with equal energies of all particles

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Fig. 3.3 Schematics of anisotropic plasma etching in non-equilibrium plasmas

the substrate especially in case of etching of the dielectrics as potentials develop inside the high aspect ratio structures that may divert trajectories of ions to side walls and even reflect the ions backwards. Problems caused by these processes will be discussed later on. In addition to etching, plasmas are also versatile and lead to numerous related applications, such as cleaning, polymerization, thin-film deposition and ashing [27, 28].

What Are the Limits: Roadmaps The industry defines goals for the next 10 years and those are given in well-defined roadmaps [29]. The idea that research may be defined so precisely seems farfetched, especially if having in mind the complexity of the technology involved. Yet, as we have all witnessed in the past four decades, it has worked and, if anything, the progress has often been faster than previously expected. The plans are made for all aspects of the technology including etching and development of plasmas. Progress and plans for progress for dimensions of connection holes and gate lengths are shown in Fig. 3.4. The progress in employing plasmas for etching is also strongly tied to the progress in photolithography and in application of new materials. Improvements are required not only in reducing the resolution but also in increasing the speed of operation (thus changes in production of interconnects and materials involved may be required). It has often been discussed just when the progress will depart from the Moore’s law towards saturation. Of course, even in that case further improvements in processing power could be achieved by improved software and hardware design or by stacking the transistors in three dimensions (3D) provided that thermal dissipation issues can be resolved. And indeed, the thermal dissipation limitations may prove to be the critical issue to be solved in future years as the voltage that is involved cannot shrink as fast as the volume of transistors where the energy is being dissipated.

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Another issue that is rarely mentioned is the problem that with shrinking sizes it is hard to see how far one can go in maintaining the properties of the bulk material in the small-size structures that are being developed. In addition to quantum tunnelling, one may be faced with the requirement for implantation of only a few atoms in order to achieve the required modification of the substrate. In that case, the location and statistical fluctuations of the numbers of implanted atoms may become an issue. In addition to those issues control of roughness of plasma-etched surfaces is going to be a limitation as it should not exceed 10–20% of the dimension of the etched structure.

Plasma Sources for the Standard Nanoelectronics Technology Capacitively Coupled Plasmas The capacitively coupled plasmas (CCPs) are mainly maintained by the input of energy to electrons from the moving sheath boundaries and by the effect of collisions on electron motion in RF field [21, 30, 31]. The electrons formed by bombardment of the instantaneous cathode dominate the maintenance of dc and low-frequency plasmas, but the so-called gamma electrons in RF plasmas contribute mainly at higher powers/current densities. It is possible to sustain plasma without their contributions. In the case where negative ions are the dominant negative particle, double-layer formation may become the most important source of ionization [32], while in the case of rare gas buffer gases, metastables may play a significant role in plasma maintenance [33]. Inductively Coupled Plasmas Inductively coupled plasmas (ICPs) have also been used very much in recent times. Their main advantage is a high density of charged particles due to reduced losses

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[34, 35]. As a result, radicals and excited states [36] are present at higher densities as compared to CCPs. This changes the properties of the plasma, facilitating ionization (by stepwise processes) and thereby reducing the mean electron energy [36]. ICPs allow special design of the coils that make it possible to achieve uniformity over large areas. On the other hand, complex geometry makes it more difficult to model ICPs unless simplifying assumptions are made. A very successful approach in this direction is the so-called ‘non-local’ model [37]. Typical issues that require further notice are the E–H transition and its understanding, the role of excited species and radicals, two-frequency operation and achievement of functional separation [38]. Nevertheless the ICP reactors seem to play a secondary but unavoidable role in the current plans of the semiconductor industry and IC manufactures.

Modelling Plasma Processing Devices In order to be able to claim that one understands the basic kinetics of such complex systems as RF plasmas, one needs to achieve a very good qualitative and quantitative agreement between measurements and predictions of the models and such models may prove to be the basis for designing plasma reactor tools [32, 39], both CCPs and ICPs [40, 41]. Development of comprehensive tools for plasma modelling [42– 45] is one of the goals which need to be completed in order to improve reactors for nanoelectronic applications. These modelling tools include the basic description of plasmas through either fluid equations coupled with calculated or measured swarm data or kinetic models. In fluid models some correction for non-local (nonhydrodynamic) behaviour of particles is required especially to describe the sheaths and regions of highly non-uniform field. The comprehensive set of data including electron molecule collisional cross sections and transport coefficient in the relevant energy range (for all energies covered by the plasma, atom and molecular collisional and reaction data for all gas molecules and their radicals and corresponding transport coefficients) is required for modelling. A number of both positive and negative ion species is usually generated and for each the cross sections and transport data are required (and usually lacking) again in the entire energy range covered by voltages applied to the plasma. In addition, parameters for surface collisions including reflection coefficients, accommodation coefficients, surface adsorption and desorption and related recombination coefficients, efficiency of inducing secondary electrons and other particles and etching and implantation rates are required for all particles. Finally, one needs to follow the kinetics of excited species, metastables and photons including their collisions with surfaces. When radicals and excited species are generated in large numbers, one needs cross sections for their collisions with active particles, mostly electrons, and their related chemical reactions. Finally, when dust particles are present their properties need to be included in the model as well. Comprehensive plasma models need to be developed to deal with complex geometries and also with external parameters such as temperatures, gas flow and loading and other issues.

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With such developments the models have achieved a high degree of reliability with the ability to treat complex systems and provide a realistic representation of surface processes [46–48]. It has been possible for example to model development of the breakdown in the insulator of CMOS FETs during the process of manufacture due to charging of dielectrics and development of the corresponding potentials [49]. These problems are exclusively associated with nanodimension of the structures in new technologies where thickness of the oxide layer is only a few nanometres and size of the drain and source a couple of tens of nanometre. The ability to deal with issues such as charging and also to predict profiles of structures [49–51] seems to be essential for applying the same models to predict the properties and the development of nanostructures by bottom-up and top-down technologies. These new challenges, however, require further improvements of the modelling and covering of some of the physics that has been poorly represented so far. Even in electron kinetics some assumptions are often made to simplify the models, that may fail to represent all aspects of important physical processes [52, 53]. Issues in basic development of the comprehensive models are the following: interpretation and accurate representation of fluid equations [54], interpretation of the transport data [53], inclusion of models relevant to describe negative differential conductivity [55], anomalous diffusion [56], the role of magnetic field in dc transport of electrons [57, 58] and resonant processes feeding the energy to electrons in complex electric and magnetic fields [59, 60]. In addition representation of time-dependent processes and spatially dependent processes not involving hydrodynamic approximation is required [53, 61]. Development of the new experiments is also needed to test complex time-dependent theories and provide the lacking data for fast neutral collisions and for negative (and also positive) ions. It is unlikely, however, that sufficient experimental data may be produced for electron radical collisions but even the small number of the available data [62] may be used as a benchmark for theories that could produce basis for modelling the role of radicals [63, 64]. Development of plasma technologies for nanomanufacturing will also open the need for the data for new gases that were not the subject of main interest of plasma modelling community, even the return to some of the standard gases that have a lot of data in the literature (N2 and H2 modelling of low-k solid-state electronics [65]).

Two-Frequency Plasmas, Pulsed Plasmas and Charging Damage It seems that CCP reactors are the most interesting type of plasma reactors for the industry at the moment. Their operation under two frequencies and even three frequencies allows a good and functionally separated control of plasma maintenance (i.e. the flux) on one hand and biasing (i.e. the energy of ions hitting the surface) on the other [66, 67]. It was found that under some conditions the low-frequency power supply which was introduced mainly to control the energy of ions was able to change the properties of plasma significantly, even to turn it on and off. Thus in spite of being there to control the energy of ions, the flux and operating conditions could

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change as well leading to a very complex and unpredictable pattern of operation. From the practical point of view one would prefer to have an independent control of the ion energy that does not affect the properties of the bulk plasma and flux of particles. In recent years some understanding of the pertinent physics of the multifrequency operation has been found although optimal choices still have not been made in the industry presumably due to existing patenting rights. It was found that optimal combination for CCPs was to have low frequency of the order of 1 MHz and high frequency of the order of 100 MHz. Recent development of micro-technologies for micro-electro-mechanical systems (MEMS) and micro-optical electro-mechanical systems (MOEMS), as well as the reduction of critical dimensions in micro-electronics below 100 nm together with increased complexity of the processors requiring nine and more interconnect layers, has brought out the need to develop plasma processes able to etch small features with very high aspect ratio (10–100) [68]. Contacts between different levels and across the surface of the IC provide functionality to the IC. As a result of the need to produce very complex ICs and at the same time to achieve minimal dimensions, the connections have to be very narrow and deep, or in other words of a very high aspect ratio. Etching of the connections is the most difficult process determining the limits of the resolution and defining the technology. Numerous ‘aspect ratio’ related problems may occur during the production of ICs. For example, due to the continuous reduction of the solid angle of the plasma from within the nanostructure (as the aspect ratio increases during the manufacture of the contact hole), the etch rate will be aspect ratio dependent and that is an undesirable effect. In addition, there are other associated issues, such as etch stop, notching and many more. Most of these problems have been strongly associated with charging of the bottom of the nanostructures [68, 69]. In principle we want to make a nanostructure of a very high aspect ratio in a dielectric. As the number of positive ions deposited at the bottom of the nanostructure increases, the potential at the bottom also increases and eventually it will become equal to the potential that corresponds to the energy of ions. At that point no ions will reach the bottom of the trench and further etching will stop. This effect is illustrated in Fig. 3.5 where

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we show the potentials at the bottom of a nanostructure [68, 69] as a function of the aspect ratio. It was found that for aspect ratios greater than 7 the potential at the bottom of the structure becomes equal to the potential corresponding to the ion energy. The potential at the side walls of the structure close to the top is small as it is defined by the energy of electrons reaching the side walls. In modern IC manufacturing plasma charging damage is more prevalent and has grown into a significant field of its own [47, 68, 70–75]. In addition to the etch stop, other forms of damage exist. For example, charging of the bottoms of the wells leads to an increase of the potential on the dielectrics of the transistors and due to very thin dielectric layer even the smallest amount of charge may induce a high voltage and the resulting breakdown in the dielectric of the MOSFET transistor. Understanding what causes the IC damage during the process of plasma etching necessarily requires both models and experiments but it may also provide a strategy to avoid charging-dependent and other problems. A solution to the charging in the high aspect ratio structures would be to have pulsed operation of plasma so that in the afterglow we may discharge the bottoms of nanostructures provided that such a relaxation of the accumulated charge is possible. After the collapse of the sheath electrons may be able to arrive to the surface and eventually reach the bottom of the structure. Temporal development of the charging potential gives the time constant of a few tens of milliseconds [68] for the potential to be developed. The real value of such prediction would be limited by the highly uncertain estimate of the charge losses in the bulk of the dielectric and on the surface. As the damage induced by charging through both etch stop and the breakdown of the very thin dielectrics is the principal cause of defects of ICs, techniques for avoiding these problems should be high in the list of priorities for further research. It will also be critical to reduce the charging damage if one wants to proceed to even smaller dimensions to true bottom-up plasma-aided nanotechnologies. Experiments with pulsed plasmas gave an excellent improvement regarding the defects that may be associated with charging [76] where plasma sustaining source is pulsed while biasing voltage remains continuous. The principal limitation of the technique to discharge the dielectric by pulsing proved to be the poor conductivity of the dielectric. Makabe and coworkers have shown that in the afterglow during a short period of time, a double layer forms that may push negative ions into the nanotrench [77] which would improve neutralization of the deposited positive charges. The influence of mask charging on profile evolution during the main etch has been considered [47]. Mask charging can influence profile evolution by directing ions to the side walls of the material thus causing bowing or leading to microtrenching. Figure 3.6 shows the electric field vectors on the profile surface in a dielectric for two different aspect ratios similar to those presented in [78]. The time necessary for the electric potential at the bottom of the feature to reach its steady-state value (Fig. 3.7) varies from less than 1 ms for the smallest aspect ratio up to 10 ms for the highest. These times combined with some additional techniques to remove the charges will determine the optimum pulsing periods that would reduce the charging problems.

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Fig. 3.6 Electric field at the profile surface for the aspect ratio of 4.5 (left-hand side) and 6 (righthand side)

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few electron volts to the etching has been recognized [79]. It has been proposed in 1991 that very high energy fast neutrals may be produced by the charge transfer in sheaths and may contribute significantly to plasma etching [80]. Subsequently, when charging damage became an issue in the manufacturing of ICs, it was proposed that fast neutral etching could solve these problems [81]. The idea of this proposal was to take advantage of charge transfer collisions to form a beam of fast neutrals and to apply a grid to stop the ions or to neutralize them even further. A similar proposal which relied more heavily on additional neutralization at surfaces of narrow tubes was given more recently [82, 83]. These techniques have been tested in production of ICs and were shown to reduce or even eliminate the damage. However, pulsing and other techniques were also sufficiently efficient for the same purpose and for current technologies (90–45 nm). Thus fast neutral etching has not been employed at the industrial level so far. It is, however, believed that it will have to be implemented for smaller dimensions as it also provides etched surfaces with smaller roughness. It was shown that 8 nm columns (quantum dots) could be made by using fast neutral beam etching [82]. This is a good indication that fast neutral beams may become essential in manufacturing of nanostructures smaller than 32 nm. We have studied the efficiency of neutralization in a realistic system similar to that proposed by Samukawa and coworkers [82] by considering collisions in the gas phase along with the ion neutralization at the surface. Surface neutralization of ions and collisions of ions in the gas were first analyzed separately and then their joint effect was determined. Calculations [84] indicated that for grazing incidence conditions it is safe to assume that the neutralization efficiency is 100%. However, it was found that the effect of gas-phase charge transfer and surface collisions in converting ions into fast neutrals are approximately equal for the conditions of the system used by [82]. These calculations were coupled with a plasma model based on particle-in-cell (PIC) method [85].

Etching of Low-k Dielectrics The need to increase the speed of the processors and memory units led to the need to reduce the effective dielectric constant of the dielectric that is used for interconnects. Transition from four to around two will suffice for the technologies that are developed now, but further improvements are required in order to meet the roadmaps beyond the end of this decade. Three approaches are considered: porous materials, low-k inorganic and low-k organic compounds [65]. New technologies for etching of such materials are required and one example would be etching of low-k organic materials where it was found that efficient anisotropic etching may be found in mixtures of nitrogen and hydrogen. While hydrogen provides etching even without special biasing, additional biasing increases the etch rate linearly. This implies that the etching process is a simple one-step process. On the other hand, nitrogen is required to provide anisotropy by passivation of the side walls. Thus the role of ions is to open the bottom of the trench to hydrogen radicals and also to provide additional treatment of the surface giving

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effectively reactive ion beam etching but with different characteristics as opposed to SiO2 etching by CF4 . Including these processes into our code for simulation of the development of structures is required for low-k modelling and in addition simulations of the etching of porous structures would be of great interest.

Plasma as a Source of Nanomaterials Nanomaterials A critical element of nanotechnology is not only the discovery and creation of nanomaterials with advanced tailored properties but also their implementation in whatever form or substrate is most suitable for exploitation. Nanomaterials, so called because their dimensions (below 100 nm) lead to special properties or additional functionality over their macroscopic counterparts, present a major implementation and delivery challenge because of these dimensions. CMOS technology has, over the past decade, successfully delivered complex nanomaterial devices and much of this success has rested on the capabilities of plasma processing. We can be confident that, in the future, plasma technology will play an ever increasing role in the delivery of new nanomaterials and nanotechnologies. Nevertheless the exact nature of this role is difficult to predict. Plasmas offer exquisite control and versatility but are also considered complex and expensive. Their uptake will depend therefore on advances and requirements for both nanomaterials and plasma technology itself. Here we present a broad brush outline of current developments in nanomaterials with a few more specific examples to highlight the potential impact of plasma technology. The term nanomaterials has been used to cover nanostructured materials with imposed nanoscale topography; nanoparticles and nanocomposites where the nanoparticles are embedded in a matrix, often a polymer; nanocapsules; nanoporous materials, e.g. membranes and scaffolds; nanofibres; fullerenes; nanowires; nanotubes, particularly carbon; dendrimers; quantum dots and thin films (<100 nm thick). Among the many synthesis techniques are self-assembly; chemical vapour deposition (CVD); chemical synthesis/solution methods (sol gel, colloidal chemistry); gas-phase methods (flame pyrolysis, electro-explosion, laser ablation); electrodeposition/electroplating; spin coating; spray coating; physical vapour deposition (PVD) including plasma techniques such as magnetron sputtering; plasma-enhanced CVD (PECVD). The delivery or implementation of a given nanomaterial depends on the actual application and will vary from the production and handling of bulk quantities, for example in the addition of nanoparticles to sun cream, to the position-critical placement of, for example, nanowires and nanotubes as transistor and interconnect elements. The nature of the particular market is of course of critical importance in determining synthesis routes especially for volume markets where both cost and

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quantity specifications are the challenge here. Nevertheless future markets for nanomaterials also include many high-value niches where simple bulk synthesis routes cannot deliver the required quality. Examples of high-value markets include displays ($90B): field emission displays, LCD backlighting with carbon nanotubes (CNTs), organic LEDs; photovoltaics ($50B): quantum dots (QD) for III–V solar cells; imaging ($10B): CMOS imager with plasmonics, IR imager with III–V quantum dots; lighting ($6B): LEDs with QD II–VI (ZnO) and high-index III–V nanostructures, II–VI QD organic LEDs; photonics: active fibre (amplifier) with nanoparticles; sensors ($4B): fluorescent markers with QD (II–VI), plasmonic biosensors, CNT-based biosensors. Without any doubt a rapid development of nanotechnology was catalyzed by the discovery of carbon nanoclusters known as fullerenes [86, 87]. The term fullerene encompasses the entire class of closed-cage carbon clusters. Their applications include drug-delivery agents, fulleride-based superconductors and light-activated antimicrobial agents.

Carbon Nanotubes Carbon nanotubes and associated nanostructures such as nanocones and nanowalls have been studied in great detail over the past decade due to their potential use in a large number of valued application areas. These range from transistors and interconnects for post-CMOS IC technology, field emission displays, high surface area electrodes in biosensors to incorporation in nanocomposites and bulk gas storage or filter materials. Originally derived from high-energy thermal (arc) plasmas, the synthesis routes have expanded to include laser ablation, chemical vapour deposition and PECVD in order to meet demanding specifications for both individual nanotube quality and, for example, positional growth. High-temperature arc and laser plasmas are under continued investigation for the production of bulk quantities of nanotubes but suffer the inclusion of high levels of metal and amorphous carbon impurities. Post-purification by chemical means is possible but can impact adversely on the nanotube quality. CVD synthesis, at high temperature (850–1100◦ C), is effective for producing moderate quantities at reasonable quality and more recently has been used to produce continuous fibres [88] of nanotubes held by van der Waals forces. Although CVD is simple and comparatively inexpensive, it is currently unable to produce high-specification carbon nanotubes, and the high temperatures are problematic for deposition onto many substrates, including semiconductors. Plasmas used in PECVD cover a wide range of pressures and frequencies. dc, RF (CCP, capacitively coupled plasma, or ICP, inductively coupled plasma, which is preferred as it leads to less contamination) and microwave have been used [89– 94]. Pressures of few hundred milliTorr are the standard for dc and RF plasmas but atmospheric pressure operation has also been tested. Numerous issues are still open and worthy of scientific effort in relation to improvement of PECVD sources for CNT growth. These include the identification of the primary precursors and the role of other particles such as atomic hydrogen in

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the growth, the role of ions in the growth and how it changes with the ion energy, the mechanism of alignment and how it is influenced by the electric field, how to optimize the substrate bias, how to achieve uniform growth over large areas compatible with IC wafers, how to control chirality of fibres and how to produce SWCNTs in PECVD production [89, 95]. Individual nanotubes are grown as single-wall (SWNT) or multiple concentric tubes (multi-wall MWNT) and quality parameters to be controlled are diameter, chirality, length and defects as well as incorporated impurities. They are grown vertically with density ranging from sparse to dense forests and here the quality of the vertical alignment and spacing between individual nanotube and nanotube bundles may need to be controlled. Applications include pillars of conducting nanotubes as IC vias or sensor probes and forests as biofluid filters, with field emission requiring relatively sparse growth to maximize the geometrical enhancement of electric field at the tip. Of course, there is a major drive to produce horizontally grown nanotubes for use as transistors or interconnects. Plasma growth techniques for carbon nanotubes are dominated by microwave sources operated at high pressure in hydrogen- or nitrogen-diluted hydrocarbon gases (Fig. 3.8) [96]. Growth proceeds, in the majority of processes, from plasma sputter-deposited metal nanoparticles which often receive separate plasma pretreatment to enhance uniformity and surface activation prior to growth. Other plasma approaches include use of RF ICP and capacitive sources, although resultant quality is generally poorer. The versatility of the structures that can be achieved from plasma growth is shown in Fig. 3.9. Here the density can be varied between sparse and dense forest with variations in microwave plasma-processing parameters and substrate conditions. Other structures such as pillars of nanotube bundles can be achieved by pre-patterned catalyst for biofluid filtering [97] while diamond spherules with high surface area can be selectively deposited along pre-patterned features [98]. For all nanotube synthesis methods, post-purification is required to remove the metallic remains of the catalyst which can be positioned at the top or bottom of each

Fig. 3.8 (a) Nanoparticle islands formed from the metal catalyst layers and (b) carbon nanotube (CNT) growth at 750 C in microwave plasma (see [96])

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Fig. 3.9 Top row from left: dense vertical forest of carbon nanotubes deposited by microwave plasma-enhanced CVD, sparsely grown nanotubes and high-resolution TEM image. Bottom row from left: biofluid filter based on pillars of nanotube bundles, diamond spherules showing high surface area (inset) and selective deposition on copper tracks

grown nanotube, depending on the choice of deposition conditions. Also inefficient hydrocarbon conversion and/or hydrogen etching during growth leads to unwanted amorphous carbon phases which also have to be removed. Typical wet chemical techniques involve strong acid treatment, and increased defect density within the nanotubes has been observed after purification [99]. Plasma treatment to remove impurities shows considerable promise in this respect using ECR nitrogen plasmas (Fig. 3.10), while there are still issues regarding damage due to high bias using standard capacitive systems [100]. Nevertheless, exploration of the plasma

Fig. 3.10 TEM image of carbon nanotube with metal catalyst nanoparticle embedded in tip (left) and after plasma purification treatment (ECR, nitrogen) where the metal has been removed (right)

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Fig. 3.11 Metal nanoparticle decoration of carbon nanotubes with Pt for fuel cells (left) and with AgCl, Ag for medical electrodes (right)

purification will undoubtedly lead to low damage solutions with systems capable of higher throughput than ECR and at lower cost. After growth and purification, nanotubes can be further treated to enhance functionality. This functionalization step is often critical in device fabrication of, for example, biosensor electrodes or fuel cell elements (Fig. 3.11). Nitrogen functionalization (i.e. attachment or substitution of nitrogen) has been achieved in low-pressure RF plasmas [101] and at atmospheric pressure [102] as has oxidative functionalization [103] while more complex tailoring has also been achieved on nanotubes in a range of forms, from powder to vertically aligned forests [104]. More complex functionalization includes embedding metal nanoparticles onto nanotube surfaces, for example, to improve the surface contact area of thin-film medical electrodes [105] (Fig. 3.11). Plasma processing, purification and functionalization are still at early stages. Plasmas will offer significant benefit once dedicated, and custom solutions (sources and processes) are developed for particular challenges in each market and application. The route to plasma success in CMOS fabrication technology provides an example. Here plasma source and process designs were constantly striving to meet an ever more challenging specification on an ever accelerating roadmap. With nanomaterials, once the current materials exploration phase has matured and priority exploitation paths determined, the process and equipment requirements can be more clearly defined. While most of the current research is carried out in general plasma systems, which draw on semiconductor processing (e.g. etching) for their design and operation, this is not necessarily appropriate for future nanomaterials processing. However, current developments in plasma science mean that sources can be tailored for precise ion energies or for selecting particular species with increasingly accurate control and can be made to operate across a much wider operating space. While theories of carbon nanotube growth are still being developed, it is envisaged that once the carbon (and other) species dependencies are more fully

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understood, then plasma sources can be more accurately designed to meet those exact requirements. This will provide reliable high-quality nanomaterials and hopefully will allow major advances in terms of significant reduction in process temperature, horizontal growth processes, high substrate sensitivity for positional deposition, catalyst reduction or even elimination and impurity rejection. Other major plasma technology developments in the pipeline include very large area plasma sources, e.g. for low-cost solar panels, and the intense research activity in (cold) atmospheric plasma materials deposition mean that existing barriers to plasma technology, namely the cost and complexity of vacuum processing, may be reduced or eliminated.

Thin-Film Nanomaterials Thin-film processing has been around for a long time but thin films fall within the nanomaterials category when their function depends on thicknesses below 100 nm. In general, controlling the three key parameters of the surface chemical composition, thickness and topography allows the possibility of transferring specific or otherwise expensive properties to a nanometre-sized coating. This makes the list of potential applications almost endless with an impact in almost every industrial sector. Most thin-film applications are linked to developments in the semiconductors industry such as thin-film transistors (TFT); large-area displays (LCD, OLED); NEMS/MEMS; planar waveguides; magnetic RAM; among others. Here the use of plasma-based tools is common and, in many of these applications, plasma film deposition, functionalization and patterning are considered capital-intensive. One area that is less capital-intensive and therefore more attractive for new low-cost plasma designs is the creation of cheap, flexible, disposable electronic devices, for example RFID tags or smart packaging. Here low-temperature and high-pressure plasma designs will need to compete with less capable but also much less expensive competitor technologies. Other areas where high-quality nanocoating will become important are glass coatings, which could become ubiquitous; low-friction or wearresistance coatings, which have almost endless applications from engine parts to mechanical or drilling tools; and even high-end applications such as hard disk manufacture; and solar cells, where nano-thin films could have a strong impact, and large returns. Here the design of efficient but very large area plasma tools is critical for enabling non-crystalline and hence low-cost silicon solar technology. Finally in the medical device sector, the creation of biocompatible coating materials and surface treatments is receiving considerable attention. These coatings can be for mechanical, e.g. low-friction hip joints, and/or biological ends, e.g. forming a barrier or anti-corrosion coating, eluting therapeutic agents, inhibiting or promoting specific cell growth. Whatever the application, providing a biocompatible and/or bioactive coating that remains viable within the body for a long time represents an extreme challenge and requires a costly and time-consuming approval process. Nevertheless the end result can have a dramatic impact on human health and there is considerable active research. The medical device industry has not embraced plasma technology

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due to its perceived cost and the high degree of expertise required. Implantable medical devices are rarely planar in geometry. In fact they represent the most complex of 3D shapes from millimetre to many centimetre dimensions. The most important challenges and bottlenecks in thin-film coatings are certainly price and production volumes. In general, most coating processes are intrinsically difficult to control (spray coating, PVD, spin coating, etc.) and if really precise control is needed there are probably limits to what can be obtained with these techniques. These drawbacks refer both to the size and (3D) shape of the substrates to be coated. Lack of a full understanding of the adhesion mechanisms between substrate and the coating as well as among multi-layers is another barrier. With chemical vapour deposition (CVD) the main barriers to success lie in the difficulty of correlation input parameters with the resulting properties which block the functionalization of the coatings to specific applications. Also the adhesion to the surface and process reproducibility, which is very dependent on the quality of the precursor material, can be problematic. As with most thin-film production methods, precise coating of 3D geometries is very difficult. The deposition rate (throughput per dollar) is considered low and the process requires very high operating temperatures. Plasmaenhanced CVD (PECVD) is considered in the same light but with the addition of expensive vacuum chambers and there is a perception that the CVD method, and hence the PECVD method, is too costly for large-area coatings and volume coatings. Whereas CVD processes, however, may not be flexible enough to achieve the required quality and are limited by the high temperature, the inclusion of the plasmaenhanced option, albeit with additional cost, may provide the only solution for many high-end applications. This is